I haven’t beat 3, but I have beat 4 and 5. I think 5 took the good parts of 3 and 4 and put them in one game. If you want her to play all of them, I’d suggest start with 3 and move her way up. If you want her to get hooked right away, I’d probably say 5 Royal.

And don’t forget Metaphor in the list!

Depends what approach does you/she have.

Persona 3 Portable - if she wants to go from the earliest possible on PC (I wouldn't recommend it though, cause Reload exists) Persona 4 Golden - if she wants to go by date and still have a lot of fun (Remake is already on its way, can wait IMO) Persona 5 Royal - for a modern full-package Persona, I STRONGLY RECOMMEND THIS ONE Persona 3 Reload - to start with remake of the earliest PC-available one

I intentionally skipped first two installments as they are much more retro and not available on PC natively. I'm a huge fan so I'm case you need any help, just let me know 😉

I'm thinking maybe 3, but that's just my bias

From gameplay mechanics and art style: Persona 5.

It's way more polished and fun. You feel the age of P3 and P4. Once she finishes P5, you can try the remasters. They announced one for P4, until it's released P3 has already one (Reload).