As a bit of background, my favorite FF games would probably be (from best to worst): 7, 10, Tactics, 13, 8, 6, 9, and then the rest kind of all tied. I also have a really high tolerance for bad stories, as I try to find the good in most games. I mean...I 1000/1000 Star Ocean: The Last Hope, despite it taking 650 hours for me personally >_>
I actually really enjoyed 13 (coincidentally, I watched all 8 and half hours of cutscenes on Youtube the other day - mostly due to hearing the Leona Lewis theme song and realizing I haven't played it since launch). The biggest complaints I've heard about the game I actually found refreshing.
"It's too linear" - Yes, the game is linear, and the vast majority of sidequests, grinding, etc. doesn't open up until after you beat the final boss and reload your save. I actually liked this, as I didn't get sidetracked doing sidequests. Also, since there is experience caps each chapter, you can't overlevel. This serves 2 purposes: 1. the boss fights remain challenging each chapter, and 2. You know when to move on and stop grinding exp, because you stop having skills to spend it on.
"There's no towns/npcs interations" - I'm fine with this, as it fits in with the story. You're a fugitive the entire game..you shouldn't be hanging out fetching bear pelts for some shop keeper.
"ugh...auto-battle" - At first I doubted this, but I actually found combat FUN to watch for the first time in several games. Besides, setting up your party and timing the paradigm shifts becomes frantic enough in the late game.
It does seem like a lot of people disliked the characters/setting/plot/battle system of the game, and to each their own. While the characters aren't nearly as memorable to me as those in 6/7/8/10, I still found them satisfactory. There were several scenes in the game that I really found emotional, despite lacking a serious connection to certain characters.
Obviously, I highly recommend FFXIII.
XIII-2....well, the combat is more fun (along with the monster-collecting aspect), but the game ruins the end of XIII for me and ends up requiring Lightning Returns to exist. It's alright, but the multiple endings and plot are rather unenjoyable to me.
Lightning Returns - Well...I haven't finished this one. I realize it only exists due to XIII-2 screwing up XIII's plotline, so I forgive the story in LR. The combat I actually felt was the most complex and customizable of the 3 and really enjoyed it, but I stopped playing the week it came out for some reason and haven't gone back. Probably will at some point, unlike XII. I've tried finishing that games 3 or 4 times...and never can get into it.