Outside of a few exceptions that are direct sequels (Persona 5 Strikers, Persona 5 Tactica, Persona 4 Arena, maybe others) the Persona games are independent from each other and can be played in any order. Persona 5 is the most popular (Get the Royal edition, it's the definitive version) but Persona 4 is good too (For this one you want the Golden edition).
Outside of a few exceptions that are direct sequels (Persona 5 Strikers, Persona 5 Tactica, Persona 4 Arena, maybe others) the Persona games are independent from each other and can be played in any order. Persona 5 is the most popular (Get the Royal edition, it's the definitive version) but Persona 4 is good too (For this one you want the Golden edition).