Aasimar: Work well as any type of 'slinger, as they have a boost to their Grit pool regardless of the path you take. The Diplomacy boost is lost on them without a trait or such giving them Diplomacy as a class skill. Plus, you can't get much more mysterious than an Aasimar Mysterious Stranger.
Changeling: They get a Grit boost regardless of Archetype but take a hit to health, which makes 'em not as good as Aasimar. Hag Traits aren't applicable to gunslinging in general, either.
Dhampir: Alucard was totally a
Dhampir Mysterious Stranger, at least when fully sealed. Can be a pain to heal, though, so you'll probably have to provide for yourself, especially with that Con penalty.
Drow: There's a reason they favor hand crossbows, they were just waiting for guns to come onto the scene and wanted to be ready to switch. Like many of the Bestiary races, they work better as
Mysterious Strangers.
Drow Noble: Congrats, you found the broken racial variant and yes, they sling better than most people. What did you expect?
Duergar: Like their psionic and surface relatives, they got deep reserves of health and Grit and are armored gun nuts. Just, for the love of whatever is holy, don't be a
Mysterious Stranger, they are worse at it then their other dwarven brethren.
Fetchling: Not so good as regular 'slingers, decent as
Mysterious Strangers. They work well as assassin types, what with their built-in stealth and escape mechanisms.
Gillman: You don't want to play an enslaved character, trust me.
Goblin: Crazy gobbos are the most accurate race out of the gate and they're the only race currently that have a Favored Class Option for Gunslingers that is actually really useful, +1 crit confirm with firearms. You don't have to pursue Critical Focus and you can laugh off the Dead Shot crit confirm penalty. If they had a Wis boost, they'd be a perfect 'slinger race.
Grippli: Perfect stats, plus a climb speed to set up hard to reach sniper points, especially in forests and marshes, where their racial Stealth boost kicks in. Deepwood Sniper, right here.
Hobgoblin: Almost perfect stats without a penalty, naturally stealthy, militaristic to have sniper corps. Fear Hobgoblin Musket Masters.
Ifrit: Good stats for
Mysterious Strangers, but that's about it.
Kobold: Play a Goblin, you won't be as crippled.
Merfolk: Good stats for Mysterious Strangers but that 5' move speed makes them all but useless. Even in an aquatic environment, nonmagic ranged combat doesn't work well there without magic intervention, so Pass.
Orc: Orc not understand boomstick. Orc smash with axe instead.
Oread: Nothing redeeming here.
Strix: Flying gunners, anyone? Both Low-Light and Darkvision, skill bonuses to hide and seek in the dark, can fly bloody fast as an extraordinary ability. Nothing not to like here.
Svirfneblin: The equivalent to the Halfling Mysterious Stranger, they have it all where it's needed and then some. Bonus to AC and saves, SR, skill bonuses out the ass, useful spell-likes. About as broken as Drow Nobles, really, and probably is.
Sylph: Good stats but that's about it.
Tengu: Near perfect stats, good skills, proficient with all swords as a a neat side perk. Just...nice...
Tiefling: Opposite side of the coin from aasimar and about as good as gunslingers.
Fiendish Heritage to be born of Asura, Div or Rakshasa stock can get you better stat array, plus the Varient Tiefling Abilities can get you up to +4 Wis or Cha, among other things, so you can truly be infernally gifted at 'slinging.
Undine: Perfect Stats and some other neat perks, Definitely the strongest of elementally descended.