Favorite RPGs you'd recommend

[Jay R]

If you like swashbuckling adventures and musketeer movies, then Flashing Blades.

It has classes that are based on actual classes. Where you were born and who raised you. You are a Noble, Gentleman, Soldier, or Rogue. In the Caribbean supplement High Seas, this is expanded to include Sailor, Marine, or Pirate.

There are five dueling styles. If you learned Italian style, your thrusts and lungers are better. Spanish style has improved slashes, etc. [The game was written in the 1980s, and there is no authenticity to the style descriptions.]

Each character has an Advantage (title, wealth, lackey, favor, contact, etc.) and a Secret (secret loyalty, sworn vengeance, secret identity, duelist, inveterate gambler, etc.). These make the characters unique, and are the key to fitting a swashbuckling persona.

The main characteristics are Strength, Dexterity, Endurance, Wit, Charm, and Luck.

The skills are a big part of the game. Each class has three skills that cost 1 point each, a set of what you might call "class skills" which cost 2 points each, and the rest are 3 points. So it costs a Rogue 3 times as much to learn Heraldry than Cutpurse. Once you buy a skill, your ability is based on the associated characteristic, plus experience. Each skill or fighting weapon goes up individually, based on how much you use it.

Social status is real, crucial, and part of what you're striving to earn.

The game's biggest weakness is, being made in the early 1980s, the assumption was that all players would be guys, and there are no female character types. I invented Actress for as player in my game, though it would be easy to play a Noble or Rogue as a woman.

It plays quickly, feels right, and lets players act like swashbuckling heroes.

[Anonymouswizard]

I am going to put in a recommendation for Das Schwarze Auge/The Dark Eye, with the cravet that it is in no way rules-light (in terms of heaviness the 5e core rules are somewhere between 5e D&D and 3.5 D&D).

In the latest edition characters are built on a point budget, with Culture and Profession packages to make it simpler. It's relatively low fantasy, magic is weak but nonhuman creatures aren't uncommon, and all elves are spellcasters. Casters are balanced by starting effectively 140-180 points behind everybody else in exchange for magic and some benefits related to their Tradition, the same for Blessed Ones (essentially clerics, who have stronger but more limited powers than spellcasters).

In addition outside of combat, and even for combat spells, every skill check is rolling 3 Attribute checks against two or three Attributes, for example Courage/Intuition/Dexterity. Attribute checks are a simple 1d20 under Attribute, and for skill checks you can use your skill points to reduce the numbers you roll.

But the key thing is the incredibly detailed world. Imagine that instead of making lots of different settings the designers of D&D focused everything on one. That's the level of detail Aventuria has. Although much of the information hasn't been released in English that (the bits that have get you to roughly 'new editions Forgotten Realms' level), but there's sourcebooks on almost every country in the pipeline.

[Louro]

I'm liking Warhammer 40k. Although the setting is pretty... disturbing.
I'm definitely trying Dungeons the Dragoning 40k at first chance.

I won't suggest paranoia. Mechanically beautiful on a brilliant scenario. Best ever game but requires some complicity between DM and players.

[AshfireMage]

To add/agree with what others have said, I think it's best to try lots of things if you get the chance- after all, you might absolutely love something that you would never have thought of normally!

That being said, here's some criteria to consider, since sometimes it's hard to know what the right questions are when you're new

1. It looks like you said you prefer on the lighter end of the "how many rules" scale, but it's a consideration, definitely!

1a. How much do you care about the game being "balanced"- ie, does it really matter to you that most options are going to be equally powerful by whatever metric you want to use? Or do you not care as long as the game functions?

2. What genre- sci fi, fantasy, slice-of-life, etc? You can get an rpg for just about any kind of story you want to tell, and it's a fast way to narrow down your options

3. Do you prefer something fairly setting-independent, or something with a setting baked into the mechanics? At one extreme, we have something like GURPS, which is designed to be completely generic- you're supposed to be able to find rules for literally anything you might want to include in your game. Others, such as the World of Darkness games, have the lore and mechanics intimately tied to each other. While changes the setting are possible, you're definitely have to make a conscious effort to get away from the published universe, and will have to make a lot of houserules if you want to do something radically different. I'd say most editions of D&D I've seen are somewhere in the middle.

3a. If you do want one with at least some level of setting established, do you want it to be an original property created for the game, or do you want it to be Franchise: The RPG?

4. If you have any idea whatsoever, how many people do you think you're likely to be playing with? Some systems do large groups better than others, for example.

5. You said you're looking to do it on the cheap, but how much money you're looking to spend is definitely a good question. Apart from free games, the cheapest usually hit the balance of "old enough that you can find plenty of used copies" and "not so old they become a collector's item"

5a. Is it important to you to have the book available in a specific format? There are numerous RPGs that are only avalible as PDFs (unless you want to go to the trouble of printing the rules off yourself), and others that aren't legitimately available in digital format. If storage space is an issue, or like me you really like having a hard copy at the table with you while you play, it's something to think about.

6. Does the idea of having a lot of additional content (be it lore, mechanical things like new classes or abilities, or both) available in expansion books appeal to you, or do you want something that's a bit simpler/broader in it's rules and/or a less developed setting, but all contained in just one or a couple volumes?

7. For lack of a better way to say it, what "content rating" are you looking for? Obviously, how it works out in practice heavily depends on the group you play with. But again, there's a spectrum. If you (or anyone you think you'll be playing with) is a child/teen or has delicate sensibilities, something like Demon: The Fallen or Warhammer 40k is probably a bad choice.

[Kadzar]

My primary recommendation would likely be Stars Without Number. It's a good sci-fi game, and the free version has everything you need to play and run the game, with the deluxe version basically just adding in some non-essential setting options. And you can use supplements from the previous version with minimal conversion needed to add in more stuff later, if you want. Or you can take things from OSR games and convert them for use in Stars Without Number (with possibly a light reskin to make them sci-fi). Or you could even run a different sci-fi game entirely and still use many of the world creation rules and adventure seeds and faction rules in a completely different system.

My second recommendation would probably be Dungeon World (there doesn't seem to be a free PDF version of it anymore, but there's an SRD kind of like what 3.5 and Pathfinder have. You can at least grab the playbooks from the site). Dungeon World sort of emulates an older version of D&D, but it's mechanical workings are a bit different. A lot of it is based on the GM reacting to what the players do by making certain moves in response, such that there isn't any sort of initiative rolls in the game; rather, making attacks or doing actions in the presence of enemies puts characters in danger of attacks. Also, there are a lot of situations where you might be required to choose one or more things that happen to you from a list, and sometimes that comes down to which bad thing doesn't happen to you. The game is based on another game called Apocalypse World. It's kind of different, but fun.

Third is a game called Mazes and Minotaurs (also here's the DriveThruRPG link, which I think has a few newer bits that aren't on the original site). Mazes and Minotaurs posits a world in which Greek mythology, rather than medieval fantasy, inspired the first roleplaying game, and basically goes wild with the notion. The collected works try to emulate not only the systems of earlier D&D, albeit with much more streamlined mechanics than early D&D ever had, but also the culture of a game that was built up over the years by magazines and supplements, parodying the odd nature of some of those additions, while also recreating the fun and whimsy of it all. And it's all free!

And I think I'll end it for now with Talislanta (DriveThruRPG Link. I'm pretty sure the site has all these and more, but DriveThruRPG has print options in case you're into that). Talislanta is a weird and fantastical setting, where you can play a bunch of different humanoid races that don't exactly have any direct analogs to more traditional fantasy ones. Like, dozens of them. Also, the system is pretty streamlined, and has a nice thing where, the more skilled you are at the task you're doing or compared to your opponent, the more likely you are to critically succeed, whereas you can't critically fail unless you're very unskilled or facing a very tough challenge. And there's 5 (main) editions to choose from, all free!

[iTreeby]

For simple R.P.Gs there are two that stand out in my mind. FATE and Blades in the Fark. What both of these games have in common is their attitude about narrative freedom and their relative simplicity

In FATE you can basically play anything that you want to as a group,. Player characters have narrative powers based on their descriptions, I liked playing vector city (a super hero style add on) very much every time I got to play it.

Blades in the Dark Is a game where failure is used to create narrative struggle. You can make bad things happen to your character for extra dice and every roll you make has a chance to complicate the situation. The default setting is fantastic, it has a very Dishonored feel to it.

[YohaiHorosha]

Some advice for the OP, beyond what was already given.

First, welcome to the hobby!!! This hobby is fun, amazing, creative, and immersive. And there are literally billions of things to explore.

To that end:
1) don't buy anything yet. Seriously, there's SO many games, and the choices are overwhelming. The volume of games out there makes categorization difficult. And you don't even know what you truly like about the hobby yet. Do you like combat simulations? Investigations? Setting exploration? I can go on and on.
2) go to conventions (cons). Lots of cons. Local, not local, online, not online. Cons cons cons. Try games. Like, lots of games. With different gms, different styles, different settings. Each time explain 1) you're new 2) you're exploring playstyles 3) you're trying new systems and setting
3) don't ever stop exploring

I'm going to echo some things already said.

1) decide what settings you want to explore. The choices are endless, but you're kinda looking at modern, low fantasy (low level tech, low level magic), high fantasy (magic magic magic), future/sci fi/space, apocalypse, horror, pulp (basically whatever world you want, except you can't google and, generally, no cell phones, so the ability to communicate over distance on a spur...so if someone is missing, you can't just text them...or if trouble is coming, you have to race to the place), superheroes, historical fiction with fantasy elements (ancient china, Mesopotamia, etc with mystical elements), -punks (steampunk & cyberpunk as examples, which tend to focus on oppressive societies and how this technology helps some people cope, some people rebel, some people oppress), weird (look, a society of vaguely anthropomorphic insects acting like sentient beings...or cats) and mash-ups (zombies meet cowboys in the 21st century, wuxia meets cowboys meets steampunk). Like, this list scratches the surface. Start with a thing you know, and go from there. Work your way thru them, figuring out what you do and don't like. For example, I prefer modern (with mid fantasy), pulp, high fantasy. My partner likes anything with horror and high fantasy. My best friend plays exclusively high fantasy. Another friend does pulp and modern only.

2) explore what you want to play. Do you want to explore, kill things, win glory? (Dnd and pathfinder are big name examples). Do you want to exist in a world that is slowly driving you mad? (Call of cthulu). Do you want to be a an investigator hunting clues to solve a crime? (Pelegrane Press/Gumshoe). There are 100s of questions about what we want to actually play that lead to specific mechanics and game systems to support it. Most systems do the things they're meant to do very very well, highlighting the type of play it's meant to highlight, but failing to do other things. For example, powered by the apocalypse (pbta) games are great at telling stories about characters in specific roles, but not great at customizing your barbarian, your 21st century psionicist, or your 25th century scavenger. Pathfinder is great at board tactical combat, but not great at finding a clue about the whereabouts of your sibling that's been captured with little evidence. Yes, you can hack any system to do anything, but mechanics matter towards the types of stories you tell. Explore roleplay types. If you realize you love combat simulation, don't play Monsterhearts (a pbta setting). If you realize you like fantasy settings but get bored by all the combat specifics, find a game and setting that fit.

3) figure out what level of crunch you tolerate. Crunch is generally defined as the number of steps you have to take in order to decide an outcome. Generalized as light, medium, heavy. People will argue what is more fun, better, satisfying, etc. Heavy crunch takes monumental effort to understand, sterotypically consulting lots of charts and rolling lots of dice, but not always
People who love it LOVE IT, but that number of people don't dominate the hobby as much as they used to. Medium crunch is generally some form of streamlined mechanics that exist, must be interacted with, but aren't the core of what's happening at the the table. Light crunch is generally a few rules, basic resolution mechanics, and get on with telling your story. Figuring out your crunch tolerance and desire is one of the hardest things in roleplaying. Scouring these forums, you see countless people dealing with crunch tolerance issues (i want more crunch/less crunch than the other players in my group).

As you explore settings, mechanics, and crunch, you'll be able to whittle down your question from "what do i play" to "i want a light crunch wrestling game focused on wrestling careers" or "i want a heavy crunch high fantasy storytelling game where combat isn't as important as other fantasy elements" or "I'm exploring cyberpunk, what's out there and what styles do they cater to?" Or "i want a gm-less storytelling game".

Best of luck!