I haven't been "living under a rock" as they say, but I have never played any of the Persona games but I want to. If you guys can suggest a really good one from the series that would be awesome!
Persona 3 is probably one of the best places to start because it is on psn fo ten bucks. If you have a vita than you can also play an updated version of Persona 4 called Persona 4 Golden coming out on Nov. 20th. You can play Persona 3 or 4 in any order it does not really matter.
I played Persona Remake on PSP, Persona 2 Eternal Punishment, Persona 3, Persona 3 FES, Persona 3 Portable, Persona 4, and Persona 4 Arena. So I played all Persona games except Persona 2: Innocent Sin. (and probably golden because I don't have a PSVita)