If your PS3 has BC, try Shin Megami Tensei. What you'll love about this series is the story. It is incredible. Way better than what you'll see in Final Fantasy or in fact, any other JRPG.
Try SMT: Persona 3 FES first since it's like the easiest SMT game I've played, but it's still challenging a couple of times. Very fun, great story, characters and soundtrack. The game also has some dating sim into it. You can go on a date, hang out at school, etc. This game will take you over 100 hours to finish including the expansion story.
Then try SMT: Nocturne. This game is awesome. A great storyline, with a powerful storytelling. You get to choose or convince demons to join your party. Each demon has their own weakness, strength, nulls, etc (if they have any of course). The battle system is pretty simple to use, but its pretty enjoyable. You need to strategize and plan out your moves ahead of time and know your enemies weakness/strengths in order to win. Dante from Devil May Cry appears in the game. With 6 different endings and over 50 hours of gameplay, this game has lots of replay value, and it'll be remembered for years for its deep meanings. You choose whether you want to save the Earth or destroy it. I must warn you, it's difficult.
If you happen to like Nocturne, try SMT: Devil Digital Saga 1 & 2 next. Persona 4 is going to be released in December. There is also SMT: Raidou, but I never played it.
