OK, so I actually know a fair bit about this series since I went through (a good chunk of) it semi-recently myself!

The mainline SMT games all take place in post-apocalyptic Japan, where your party is yourself, maybe a few other humans, and most importantly, demons that you recruit, level up, and combine together to make new, more powerful ones. Like someone else said, SMT is sort of like Pokemon, but instead of fighting with cute electric rats and furry bait, you fight alongside various mythological figures (...and furry bait). The SNES games are first-person, grid-based dungeon crawlers, but later games largely drop the grid-based aspect.

Anyway, I started out with Shin Megami Tensei 1 on the SNES. It was pretty darn enjoyable, though I used a walkthrough--if you play the SNES games, I strongly recommend doing this, because both games are basically one giant labyrinth with an overworld. A walkthrough is pretty much mandatory to navigate which demons are worth recruiting and merging together, and to find the various secrets and treasures scattered throughout the world. A nice thing about the first game is that the level scaling is well-paced; as long as you don't run away from battles and are smart about your recruitment and demon fusions, you should generally be able to keep up with the power level of your enemies.

As for SMT 2... well, it spikes the difficulty up much higher than the first game. to the point where I actually wound up giving up about 10-15 hours in, even with a walkthrough and using save states. I had reached a point where the enemies were outleveling my demons and killing them over and over, I couldn't easily afford to revive them, and I was having trouble recruiting new demons to merge with my existing party into more powerful ones--there were multiple instances where even when I used save states to explore the demon's entire recruitment dialogue tree, it either took my valuable items/money and ran away, or attacked me. Forced to choose between sitting and grinding for at least 5-10 hours, or moving on, I moved on.

SMT 3 on the PS2 is the first real "modern" shin megami tensei game, and it introduces the press turn mechanic that forms the core of the mainline SMT series from that point on. Press turns work by giving each side a number of actions they can take based on how many members are in the party--in other words, if you have 4 members active in the party, you have 4 actions. If you hit an enemy's elemental weakness, you're given bonus actions you can take (up to a max of 2x your base actions), and if you miss an enemy, or attack them with an element they nullify, reflect, or absorb, you lose turns. Crucially, this also applies to your opponents as well, making combat tense, tactical, and deep: your demon is the only one that uses ice magic, which the enemy is weak to, but your demon is weak to lightning and the enemy can use that element. Do you switch out this demon to cover your own weakness, or keep it in to better exploit the enemy's weakness? Remember, if the demon dies, you not only have to spend a turn summoning a replacement, but your baseline actions go from 4 to 3, so you're penalized twice.

Admittedly, I didn't play SMT 3 myself, because it has That One Fucking Spell called Beast Eye, which is something only opposing demons can use, and spends a single action to grant the AI two turns (or Dragon Eye, which grants four turns). This gives SMT 3 a reputation for being incredibly difficult, even by the standards of SMT, and frankly I had no appetite for that after having just given up on SMT 2 over difficulty. That said, everybody I speak to who has played SMT 3 says that it's one of the best RPGs on the PS2, however, so it's still highly recommended, and later games mercifully got rid of Beast/Dragon Eye.

SMT 4 is... odd. It starts out looking like a much more generic fantasy setting, but it most assuredly is not. It's good, but it also very clearly is straining against the limits of the system it's on. SMT 4 Apocalypse is also extremely good, and I would suggest playing SMT 4 just to play SMT 4 Apocalypse. I won't say too much about SMT 5 except to note that it's also good and I recommend it strongly.

There's also Persona. Where SMT is a post-apocalyptic dungeon crawler, Persona (at least from 3 onwards) focuses much more heavily on time management. You play as a Japanese high school student in Persona, so a lot of your activities are based around juggling a schedule: attending classes, going to after-school activities, working part-time jobs, spending time with your various party members to build relationships, and saving the world in between. Persona is also different in that instead of having mythological figures fight alongside you as distinct party members, they're instead Personas that act more like Stands from JoJo's Bizarre Adventure--they just give humans the ability to cast magic. Notably, the main character is typically the only one who can change their persona-- your companions all have their own persona, but they're stuck with the one they have, which conveniently gives them their own static elemental strengths/weaknesses and roles. The other big difference is that (up until Persona 5) the main dungeons were more roguelike, procedurally-generated designs, than the static designs of mainline SMT.

If you decide to play Persona, I'd start with Persona 3--either Reload (the recent remaster) or Persona 3 Portable (which has some extra content like that wasn't included with the remaster for some godforsaken reason). DO NOT start with Persona 5 like I did--to be blunt, it's way more polished than 3 or 4, and it'll be hard to go back and enjoy the previous games afterwards. You can also technically start with Persona 1 and 2, but they're waaay different than the later entries--they lack the time management/dating sim aspect entirely, and honestly there isn't a whole lot of reason to play them unless you wanna beat the shit out of Hitler for some reason.