Before watching the Endurance Run, I made a decision to avoid the Persona Games because I didn't like the idea of playing a high school sim. So, while I was already a fan of the SMT games, I didn't decide to buy either two PS2 Persona games until watching Jeff and Vinny wander their way through the wacky world of Persona 4.
PS2 is really where it's at for jRPGs. Any of the SMT series is great, but they can be a little to frustrating for someone just getting into the genre. Unfortunately Final Fantasy is probably the best series for someone just starting to get into jRPGs. However! while the FF games are generally piss easy and have generally pretty user friendly game play, their stories and characters are far behind the sophistication that you'll find in the Persona series and the SMT series as a whole. If you must play any of the Final Fantasy games (and Square-enix games in general) I would suggest getting the DS versions of FF3 and 4 and maybe Chrono Trigger. They're pretty easy to find, a bit more channeling than their current console counterparts (alliteration bonus), and more "dungeon-crawler-like" which they have in common with Persona 3 and 4.
Avoid Final Fantasy X, unless you want an incredibly dull end game. (I.E. you can one-hit the final boss from just doing some of the side quests.) It's a very broken game with story that is disappointing due to it's uneventful and uninteresting ending.