I played some of the Main Series excluding I, II, V, VI, XI (That's quite a lot actually, lol)
Heck, I was only 3 when X came out >.> Couldn't play XI because of Age requirement.

I also played some of the non-main series:
(FFT Series, FF Type-0, XII Revenant Wings, X-2, Crisis Core, Crystal Chronicles, 4 Heroes of Light, Dissidia series)

As for the order/consecutiveness, No I didn't play them consecutively, and the Order was quite scrambled