Does your board support Crossfire or SLI (if that's something you might want to do in the future) or both?
Definitely only get the "TI version" if you get the 560 (the non-TI is a different card and more comparable to the 6870). A 2gb card will have more room for textures, so would be better for gaming above 1080p (and slightly better at that res).
OCing potential between 1 and 2gb cards should be the same. Between the 560 TI and 6950 is a toss-up OCing wise - it really depends on the model you get. If you want to overclock, make sure you get one with a good custom cooler, not the reference design (for either board).