Personally, if platform doesn't matter Id say 4 golden, 3 Reload, then 5 Royal. Purely from a mechanical and dungeon standpoint I think you will progress the most naturally from worst to best from there
4 Golden is now the oldest "modern" Persona game, I personally feel that 1 and 2 are just a little too old for you to get as much out of them as 3 forward, but that's my take, if you're very tolerant of older games you may wanna start older. Each entry has an independent story and characters, so I don't think that order matters as much as the progression of quality of life and dungeon mechanics.
I haven't played 1 or 2 personally but would echo what is being said here for the rest.
I played p4g first and fell in love with it. P3P is pretty similar really but with slightly less QoL things going on but I don't find it too much of a downgrade to be honest.
Either way each one has its own story then with similarities like in spell names and the like, similar to how final fantasy is.