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With current AMD X2 processor's, they all use the AMD socket referred as AM2. Some of the newer motherboards have socket AM2+ which is for the newer quad-core Phenom processor's. These are pretty much the same from the physical stand point, meaning they fit the same processor's. The only difference is that the AM2+ speed's up the quad-core's, but doesn't give a boost to dual-cores (it doesn't slow the dual-core's down though). Since you're getting a dual-core it doesn't really matter if you go with socket AM2 or AM2+. Just make sure the processor you're looking at uses socket AM2 or AM2+, and then find a motherboard that uses AM2 or AM2+ (like I mentioned before, they're interchangeable both ways, but you may be better off just going with an AM2+ motherboard).
The standard size for cases and motherboards is referred as ATX. There are some variations though, such as micro-ATX. This is a little smaller than regular ATX. A micro-ATX motherboard will fit in a regular ATX case, but a regular sized ATX motherboard won't fit in a micro-ATX board.
I don't know of a specific motherboard to get, but some of the better companies are Asus, Gigabyte, and MSI. There's others, but these are probably the best three. You may want to look into getting a motherboard with an AMD 780 or 790 chipset. They usually have good feature's and the best integrated graphics.
I hope this helps, and if you need anymore help, let us know!
"I think there is a world market for maybe five computers." - Thomas Watson, Chairman of IBM, 1943