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.