Well, here's a few starting tips.


Crew members (engineers and scientists, and to a degree soldiers) are very important. other resources like supplies, elirium, alloys and whatnot are good, but only when you actually got things to do with them. you want crew to tech up and excavate (and go on missions) especially with the expansion-you need manpower.


Teching up-don't rush the "objectives" too much, they can wait a bit. you need tech to make you stronger first. any "passive" upgrade is worth a lot more (mainly an expansion thing) as it costs nothing to benefit from it. unlocking new rooms is pointless if you can't actually build anything at the moment, and unlocking new gear isn't helping if you can't afford said gear.
Basically, when choosing a tech you should think "does it help RIGHT NOW?", and "is fast to get?" if both answers are yes, take it. if not, then don't, unless nothing qualifies-then you can go for something that takes longer.
Do not bother with autopsy unless you really need them, once you rank enough kill of that type they turn into instant research.


Building up your avenger-you got 3 types of things to excavate, regular debris, machinary and power coils.
Teh important ones are power coils-they actually do stuff other than giving stuff when you excavate them.
Any room on it takes no power, and a power relay built on one is greatly improved. the only rooms that take more power than the improvement to power relay provides are the upgraded versions of shadow chamber and the improved psi labs-two really late game rooms.
So just rush to the power coil, build a relay on it-and you'll have a healty supply of power for any rooms you want to build.


Get the guerrilla tactics school up fast. it has upgrades to squad size-and you REALLY want these.
Proving grounds (unlocked after officer autopsy) is pretty darn good, but it takes a lot or resources to feed to it in order to gain the benefits, so I would not bother rushing it.


I'll say it again-do NOT rush "objectives". they sometimes trigger alien escalation, and if you are not ready for it, it will be painful.
You have more time than you think. avatar progress can be pushed back later.