>>2460425A bit of a warning, though - if you play 5 first, it will make the older games much harder to get into, imo. 5 refined a lot of gameplay stuff, and it was a huge jump up in graphics, too. It makes the other four look like garbage and some of the gameplay is needlessly frustrating.
I will say that if you want to play the older ones, definitely get the PSP re-releases of Persona 1 and Persona 2 (2 is split into two games - play Innocent Sin first), Persona 3 Portable (PSP or Vita) and Persona 4 Golden (Vita).
None of the spin-off games are necessary, but if you like the P3 and P4 cast they are at least entertaining.