If you want to experience a truly fantastic story, Persona 2 is a must. I personally think it's the greatest video game story of all time. It's very mature in its writing and the characters feel like genuine people instead of the usual RPG archetypes. It's split up into two parts; Innocent Sin and Eternal Punishment, and they should be played in that order as EP picks up where IS left.
Persona 3-5 have better gameplay, but the storylines and writing pale in comparison. They're very anime and focuses more on their dating sim aspects, resulting in the story feelings sometimes out-of-place and the characters won't develop organically as all their character development goes into their "Social Links", basically side stories.
Persona 1 can be skipped for the most part :p
Which is your favorite FF? :D