Here's my timeline of experiencing, not necessarily beating the games. But all the games my brother beat, I came back to.

Saw FFVII beaten by my brother, then I played it.
Same order next with FFVIII.
Saw my brother beat FFIX.
Saw my brother beat FFX.
I then beat FFX.
My brother and I then together beat FFXII.
I then beat Crisis Core.

My brother came back from college and we demolished and almost mastered FFXIII together in 5 days, which was an impressive feat because it was during Ramadan and double day football practices for me and he was studying for his medical license exams.

After a two day break, I was on the PS Store and saw FF Tactics and was like, "Bro, how come no one shows this one love?" And he was like, "Please....This game is one of the best FFs and is amazing."
He played it in front of me once to see how the game works, I got hooked on and beat the game.

(Sidetrack: I also played Xenogears for my first time right after this. It was a great summer.)

Then I decided to beat FFIX, because I never gave it respect before.
And I just started FFVI this month (Just beat Atma Weapon up at Kefka's Tower )