Nocturne - Hella old school, but damn good. Light on story, but the gameplay is some of the most refined you'll find in a turn-based RPG. Might not be a good one to start out with, because it's going to kick your ass if you aren't familiar with how the Press-Turn system works in the PS2 SMT games. Still, it's worth picking up while the reprint is still available.
DDS - The first game was really good, but the second game was insanely good. Way more story-driven, and the plot is really good... though most of the plot is in the second game, so if you're expecting the story to blow you away immediately upon starting DDS 1... well, it won't happen. Definitely worth owning, though I'd put this one below Nocturne overall.
Devil Summoner - I actually finished this one, though it took far longer than it should've, because I kept getting bored after playing the game for 10 minutes. This replaces the turn based combat system with a generally ghetto-feeling real-time system, and it sucks. Enemies are annoying, and there's no depth to the combat. The game tries to make itself into an adventure game of sorts, too, as there are some areas that "puzzle" you by requiring you to have a demon with a specific skill to proceed. That's stupid. The story sucks, too. Basically, this is the only PS2 SMT game that you can go wrong with. Don't buy it, don't rent it.
Persona 3 Fes -
ing great. Only game that has addicted me enough to play 64 hours in a week. It was insane, and I'd gladly do it again. Definitely easier than either DDS or Nocturne, so it's a good intro in that regard, and it doesn't feel as relentlessly old-school in the dungeon crawling (no trap floors and such.) The school aspect of the game is off tha chain. I'm glad they went a different route with Persona 3, because another game that plays like Nocturne would've felt a little stale... but alas, this is fresh, it's unique, and yeah, it's what you should get first.
I'd also strongly consider Persona 2 for the PS1... I'm playing through it now and it's looking like it could potentially be the best SMT game of all. Basically, the only SMTs to avoid are Devil Summoner and the original Persona. I know it's not much of a recommendation when I'm saying you should buy almost all the games in a series, but they're really that good.
Man, it's nice to see the SMT series getting so much attention these days.