FFXIII for sure, 3d dot is good but given your limited time and the fact XIII-2 is due so soon I'd go with that.
As for Skyrim. I too heavily disliked Oblivion (it is my 2nd worst game ever imo) but played skyrim (ps3 mind you) because it was an xmas gift. I find it 'slightly' better (when it ran) but it had all the same problems imo (its my 3rd least favourite game ever, personal opinion & experience here). Be warned, despite the hype, its a largely similar game, just brighter & less sparse (both good points but all the other old problems are still there).
PLAYSTATION NATION LADY OF JRPGS
Favourite Games of 2013 1.Tomb Raider(PS3) 2.Atelier Ayesha(PS3) 3.Virtues Last Reward (Vita)