If you want a more traditional game, start with Shin Megami Tensei V, the newest of the mainline series. You're generally safe just jumping in with the newest entry, they're not exactly the most heavily connected plots. If you dig it, you can always give the older titles a try!
They're turn-based RPGs(with a bit of a twist), but the main gimmick is that you can recruit enemies to come fight for you. Different personalities like different kinds of things, you have to work it out. You also can unlock ways to resummon and fuse demons to make more powerful demons, some of which are bosses(and deities. Like, Yaweh and Lucifer aren't unfamiliar faces at times in the series).
SMT: Persona is a sub-series that shares some likeness to the mainline(same demons, demons becoming a form of party member, resummoning and fusing), but takes place in the "modern" world. They also focus heavily on forming bonds with your party mates. While not unfamiliar to the SMT series, the Persona titles really bring it to the forefront.
Start with 3, 4, or 5. FES(PS2)/The upcoming complete edition for the remake, Golden, and Royal are the "complete" versions of each title, respectively. This is becoming the norm of the series, a base version is released and then an updated version with extra story content is later released.
If you get really curious, SMT 1 and 2: Innocent Sin/Eternal Punishment(It's two halves of the story for 2) aren't unplayable, by any means, but I would recommend having a guide on hand. They're much less polished than the later titles.
That's really the best I can think of for the "default" SMT titles that most would recommend, but other side titles like the Digital Devil Saga games have their own fun twists on the weird world(s) of the SMT series. Just remember that they're often some form of turn-based gameplay, and when dealing with earlier titles, notoriously difficult/grindy and occasionally obtuse. You're meant to take advantage of every weakness, exploit every option, but it will be returned onto you. Luck plays a huge factor in a bloodless victory or a total party wipe, though careful planning can give you an edge.