I started with Persona 'Revelations', and I've played(and loved) every US released game since, and a few of the imports(Soul Hackers, Innocent Sin).
I agree with Eusis, though about demikids, the japanese devil children games were substantially better than the two demikids we got in the states from what I remember. they had like, storylines and stuff.
I thought the DemiKids games had a good story. Nothing like Nocturne or DDS caliber, but better than I expected.
Nocturne's my favorite. I never actually beat it though. I got up to the last dungeon, and could beat it any time I wanted, but I guess, subconsciously, I just don't want it to end.
Though, I never DID do the Amala Network...
You need to do that right now, especially the Amala.
All the best story segments are in the Amala.