>>29979423SMT and Persona are two different beasts, the latter being a spinoff of the former.
None of the numbered Persona games are related besides the two Persona 2s so you can play and skip any of them as you see fit.
Persona 1 and the 2s have not aged gracefully. 3 is widely regarded
on 4chan and its similars to be the best in the series, specially its expansion, FES. It's darker in tone than both its successors and has a pretty engaging plot, though some characters are hit or miss. Expect deaths of important characters and a main cast that borderline hates each other up until certain turning points.
Persona 4, also known as Japanese Scooby Doo, keeps a sinister plot but with much lighter and happier overtones. It plays better than 3 and jumpstarted Persona's popularity in the West but the plot and atmosphere took a blow.
"Mainline" SMT games are much harder and often more primitive than their spinoffs, making for an intense and engaging experience. Get ready to think about your next move even in random encounters and save often, lest you patoru like a bitch. Nocturne is considered the best, but 4 and its pseudo-sequel 4A are serviceable as well. Honorable mention also goes to the amazing Strange Journey, an odd non-numbered entry that plays much like the classic SMT games on SNES.
Devil Survivor and its sequel, strategy RPGs for the DS, are also challenging and fun, but simpler to dive into than mainline games. In my opinion, 2 is less interesting than 1 and feels "cheaper" in some areas.
Other spinoffs include the Raidou Kuzunoha games and Digital Devil Saga, but I haven't played either for long enough to recommend them.