I'm a lifelong JRPG fan who's played just about every 16 and 32 bit RPG there is. Massive fan of anything Square, can tell you just about anything about the first 12 Final Fantasy games, etc. I've even beaten some really obscure shit like Paladin's Quest. But one series I never played was SMT.
First off, the only way to play almost all of the games in English is fan translations, and I tend to shy away from that sort of thing because they're often crappy. So if there are any really good translations out there, that'd help.
Second, they had a reputation for being grindy. I can handle a certain amount of grinding. Dragon Quest games are about where my limit is. I like DQ for the most part, but I don't like walking back and forth just outside of town, mindlessly mashing "A" for hours, and most of them devolve into just that around the halfway mark. I haven't played anything newer than 5 though, so that may have changed over time. Basically, if SMT is any less grindy than the early DQ games, I'm good to go.
Third, I don't really know where to start. I've got forty years of content to sift through. Do I play the DDS games? Do they hold up? I'd be playing the SNES remakes, almost certainly. How about the side games like Nine and If?
Oh, and for what it's worth, I didn't like Persona 4 at all. The level design was insanely bland (nothing but identical hallways) and the battles were too easy. But I've heard P4 is the least SMT-like of the Persona games, so that might not be a problem.
You're better off comparing with Pokemon. You capture and make a party of demons with various skills. As far as the Persona vs. SMT difference:
SMT: 1 hero, who is an active battler himself, and a party of captured Demons.
Persona: A party of allies, each with one Demon/Persona bound to them, which (after Persona 3) grow in strength as you deepen your bond with your allies. The main hero is a "Wild Card-" while they do have a default Persona, they are able to switch their Persona in battle. In 3 and 4, demons can be more of an item drop, but 5 brought back SMT's negotiating system since the enemies were the Demons themselves rather than generic Shadows in 3 and 4.