You can start with either 3 or 4 since they're not related in terms of story. Just keep in mind that starting with 4 may set you up for just a *slight* amount of disappointment when you play 3 because it has tighter game mechanics overall. If you can get your hands on them, I would cautiously recommend 1 and especially 2. They are fantastic games, but brutally difficult and much, much more punishing than 3 and 4. And if you have a PS2 or PS3, I would strongly recommend Shin Megami Tensei: Nocturne. Persona series is actually a spinoff of the Shin Megami Tensei games which have been around since the 80's and Nocturne for the PS2 is a freaking masterpiece. You can purchase Nocturne from the PSN store.

No start with any Persona just don't start with Q it has spoilers for Persona 3 and 4 I say play both of them first before you play Persona Q