I agree that X is probably a good place to start. It's the first FF game that I actually finished. VI and XII are my personal favorites, but I agree with the above comments that might be a bit daunting for those new to the series (XII was straight-up overwhelming the first time through).

IX might also be a good choice; it's not as polished or as straight-forward as X, but it offers a good blend of new- and old-school goodness. Plus it's hard not to fall in love with the cast.