I know you said you've already watched FFIX, but I honestly recommend playing through it on your own, too. Ditto for FFVII. IX is my favorite of the series so it's really dear to my heart. I'd actually rank my top three as IX, VI, and VII. VIII is great, too, but definitely on the weirder side and the combat/magic system didn't appeal to me as much. I love X, as well, it has a great story, music, and characters. From personal experience, a lot of people I've met have had VII or X as their first FF. VII was my first, personally. I was very young and impressionable when it came out and it was my first RPG, so it has that special spot in my gaming memory.
So I would start with IX, VII, and X, if you don't mind playing through a game you're already watching.
Speaking of Square RPGs and Chrono, have you played Chrono Trigger?