Since you're interested in the social aspects specifically, I'd say Persona 5 Royal is probably a decent place to start.
It seems people overall have kind of soured on that game over the years, but of the modern trilogy, I still think it nails that aspect the best.
That said, P3 and P4 are good choices as well, can't really go wrong in that regard. If you end up going with P3 though I'd recommend P3Fes over P3Reload though - while pretty to look at, the remake sanded all the interesting edges off of the experience.
If you want a good story, then the Persona 2 duology is still the best game in the series though.
For gameplay meanwhile I'd recommend a game that might not be part of the series, but might as well be - Metaphor: Refantazio.