I wouldn't let anyone's opinion sway you on which entries to play and which ones to avoid. One man's turd can be another person's treasure, so they say, and I've seen plenty of people play and love FFXIII despite plenty of insisting from others that it's an irredeemably poor game. I personally would not ever recommend FFXIII to someone as a must-play game due to my own subjective bias, but on the flip side I would never dissuade someone from wishing to give it a shot. Go have a short preview of a game online and if you're interested in what you see, give it a shot.
And the MMO games allow you a free month trial (there's a limited 2 week trial for FFXIV on PC, and I'm not too sure what FFXI has) before they coerce you into subscribing. You can easily sink in a hundred hours in a month if you so wish.
I'd play X-2 just because it has some of the best gameplay in the franchise.
Listen to this person. FFX-2 immediately following the ending to FFX is quite the tonal shift to stomach, and I know plenty of fans have ever been able to wholly adjust, but if you can look past its veneer, there's plenty of the story to get invested in after the first couple of chapters. Then you have a brilliant job system that you can change on the fly, and one of the best battle systems in an RPG.
Yeah, I'll defend FFX-2 until the day I die.