To add to tinmann's post, the form factor (mATX) is what makes the determination. That is to say, all ATX cases can house any ATX mobo, as well as any mATX mobo. However, mATX cases can only house mATX mobos, as the standard ATX mobo is too long.
The difference between form factors, in a nutshell, would be the orientation of the I/O panel. For example, an ATX mobo, when looking at the back, will have the I/O panel at the left side of the mobo. Whereas a BTX mobo will have the I/O panel at the right. As you might guess, that's also what differentiates an ATX case from a BTX case.
If reusing old parts, ensure that the mobo supports the technology's generation. For example, if reusing DDR2 RAM, ensure that your mobo supports DDR2. This is important because DDR3 and DDR2 both have a 240-pin layout, but the gap between the pins is not in the same place.
Generally, AMD builds are cheaper, with fairly lower performance benchmarks. If you're looking to build a system for gaming, I recommend at least a quad core CPU, this would be AMD's Phenom II X4 line.
On the other hand, if you're looking to build a system that can handle some general clerical work (word processing, web browsing, etc.), then a dual core CPU would do just fine. You could even go for a triple core CPU for that little extra "umph". These CPUs would be AMD's Phenom II X2 or X3; or even cheaper, their Athlon II X2 or X3.
If AMD is not your cup of tea, then for gaming, I'd recommend an i5-2500k. Or for office/administrative work, the i3 series would do.