So, this will be my first dip into the realm of all things FF.
FFX is not a bad place to start. It's a great game for some, but for others, it marked the "downfall" of Final Fantasy. Personally, it's in my top 5.
But yes, please do play FFX before jumping into X-2.
Now, if you want to expand to other titles, I personally would recommend FFVI (best played on the SNES/GBA though) and FFVII
Now if you like FFVI, check out FFIX, which is a love letter to FF games pre FFVII
Now if you like FFVII, jump towards FFVIII (which in my opinion is the best out of the PS1 era)
But if you liked both, then choose your own path.
As for the newer titles if you ever venture into them, go into XIII with a open mind. XIVARR is also a great MMO. XII is also a great game in it's own right.
Then if you want to check out some of the spinoffs, check out Crystal Chronicles. I personally like CC on the GC and Echoes of Time on the DS.