Does the gun at first level have to be appropriately sized for your character?
Although i don't think that there is a rule against it, i have to say yes it has to be.
Okay so I have a few questions about the gunslinger that I did not find to be answered already
Dead shot, is there a reason to take this over vital strike other than the fact that it is a deed instead of a 3 feat chain?
Does the gun at first level have to be appropriately sized for your character?
Dead shot is A) something you get for free, and B) something that decreases your misfire rate pretty significantly (where vital strike does not). Furthermore, if I remember right, it increases your crit chance, and is further modified by the "Mysterious Stranger" archetype (though the amt of grit you have to blow to capitalize on this fact is obscene).