very fire pony. i love 
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hey so if u want to get into persona, there isn't really a necessary order to getting into it. (i havent played p3 sorry but ill mention it) all of the games have their own individual storyline, with cameos/references to the previous games but they aren't major enough to have to have played/watched them.
persona 5 is the most mainstream and (subjectively) the one with the best gameplay, so if those are the aspects you're looking for, i recommend to start there - most people do! persona 5 royal is an extension of p5 vanilla, with 2 extra main characters, and it adds a lot to the story, so i actually recommend this instead of the base game - unless you want to play/watch both.
if you're looking more for story wise, i recommend persona 4 and persona 2, where the story is more significant than the gameplay (p2 is personally my fave despite its old gameplay style and.. questionable main boss...) these two focus heavily on the characters involved and how the events of the game affect them. persona 2 has two games - innocent sin and eternal punishment (in that order), and they both have different protagonists. (fun fact! p2 is the only persona game where you can romance the same sex as the protagonist 
tatsujun 4lyf)
like i said ive barely played p3.. but if you're looking to play that, then i recommend somewhere inbetween p4 and p5, or before or after both IDK. but those 3 go well together. p1 and p2 also go well together, as p2 has characters from p1 in it, but it has introductions if you didnt know them before, and not major enough spoilers.
persona 1.. i do enjoy the game's characters, but the gameplay is really bad.Take my word for it you're humping walls more than you're progressing... it's easier to read the manga..
there are other persona games (like persona q and the dancing games blablabla) but they don't add much to the main plot, and can just be enjoyed at the side.
hope this helped!! have fun traversing on your persona journey and please dont become one of those people who say "i like persona 
" and you pretend that p1+2 dont exist i kill myself everytime i see people like that ok thanks bye