Well if I had to choose between those. I don't think I would choose either at this point in time. But if you really had to choose. 1156 would be my choice. But that's because the i5 760 is/was a great chip at its price. Currently the 2500K smokes out any 1156 and 1366 chip above or below its price.
So I would choose the 1156, but because you have a somewhat large budget. The 1366 would be good as well.
What do you mean natively? I mean it seems to run like a Hackintosh quite fine from what I've seen.