There are only 3 games really. All these various versions are just cash grabs because Atlus loves selling same thing multiple times.
Go to Persona 5 Royaj for p5, Persona 4 Golden or the upcoming remake for p4 and for Persona 3 Reloaded or Persona 3 Portable for p3. It doesn’t really make sense to play multiple versions of these games, unless you are super invested in the mechanics, and installments 1 and 2 are quite different games.
Once you’re familiar with these and want to spend more time with the characters, you can try spinn-offs like Strikers or Tactica, but bear in mind they are quite different from the main series.
If you like collecting and fusing demons go to other Shin Megami Tensei games (I recommend SMT3 Nocturne and SMT5 Vengeance). If you want more supernatural high school drama, try PSP version of Persona 2. (Perhaps 1 too but i haven’t played it yet.)
I may be quite off topic but I really don’t get all the comparisons of Yakuza Like A Dragon to Persona series. It sure is an RPG but its battle system is so goddamn boring. There are aspects of building relationships with party member but it so mediocre I didn’t feel I have any impact on what was going on, as if I watched some plain cutscenes and there is no time management aspect. I really wanted to like this game but i ended giving it up halfway because I just wasn’t having fun.