Final Fantasy X HD is the way to go. I wouldn't personally bother with X-2 yet, as it was a pretty weird step for the series, so just stick with X, it's easily one of the best in the series, if not one of the best games ever made. Then after that, try and play Final Fantasy IX, it's also one of the best games out there, and it's easier to get into than VII because it still looks stunning due to its art direction.
Avoid XIII, XIII-2 and Lightning Returns like the plague. The drop in quality was ridiculous; everything that made the Final Fantasy series so strong and iconic was removed, and replaced with nothing of value. Shallow, boring, mediocre games, the lot of them.
So:
FFX
FFIX
FFVII







