My favorites are FF 2 and FF 7 (I only go by proper American numbers because those are the only ones that matter).
I played them all since FF1 was released on NES and while that was quite a revolution, it has not aged well. FF2 (SNES) was truly special, and while FF3 was great, it never captured the magic of FF2 for me.
FF7 was another monster entirely. I think the praise it gets is totally legit, but I think it's also the last great FF game. FF8 was a disaster in story and gameplay (the card game was fun, but the magic system was complete horseshit--hey, let's create a system that almost encourages you to never use it, because getting back to 100% is another tedious grind every time you cast a high level spell!)
FF9 was a gem, however, and very similar to the old FF2/FF3 games. Story not as great, but it was very competent return to the games that made the series great.
FFX had some fun moments--the battle system was great, but leveling/ability scheme was fun, until every character became equally overpowered (some valid complaint for materia in FF 7). Auron character was pretty awesome but the rest of the game was a turd. shitty characters, stupid story....the true beginning of the end, imo (unless you could say that was FF8, which is fair)
I'd suggest going with FF2, 3, 7, and 9. If it isn't an American number, it doesn't count.