HiTechObsessed :
I will still save your money and get the 2GB card, or get the 280X. Since you can't SLI on that motherboard anyway, the 4GB card is a waste of money, when you can get the much better 280x for the same price.
Any card discussed here will fit into your system.
What HiTech is getting at (I think) is that you can't usually use more VRAM unless you have a very high resolution, which also would require a faster GPU than the one that comes with the 770 or 280x. Unless you have a specific use in mind for the VRAM (e.g. multiple monitors, or one very high resolution monitor), you probably won't use the additional memory.
As for the 280x vs the 770, the cards are very similar. If you are going to consider the 280x, just read reviews and (most importantly) benchmarks for the games you intend to play
using the settings you intend to use.