Custom PC

Part sizing is standardized, so as an ATX case it must accept all standard ATX parts. You shouldn't have any trouble with getting a motherboard that won't fit, for example. PSUs are the same way.

The type of PSU you need is dictated by a couple of things. First of all, you need to make sure that you get one of sufficient wattage to run all the peripherals you plan to include. Particularly powerful video cards these days have a significant draw as well that you will need to account for.

As far as mandatory motherboard features goes, for the most part a motherboard is a motherboard. Some will have on-board RAID which you may or may not want, or SLI, and so on. Beyond that, though, most motherboards are pretty similar in terms of features. You'll want to make a decision on the motherboard based more on stability and other characteristics you value, such as how well it overclocks, if that's something you're interested in.

CPU compatibility is straight-forward. Just look at the CPU you want and it'll say what kind of socket it takes: socket 775 or AM2+ for example. Then just make sure your CPU and motherboard use the same socket.

Additional cabling is really variable. You can basically count on some cabling being thrown in with the motherboard for connecting hard drives. If you get a motherboard with SATA (which you almost certainly will) you'll have some SATA cables thrown in but will need to likely purchase (or steal from your old machine) some IDE cables to hook up optical drives.

Jam it back in, in the dark.

A 500 might be a bit low depending on how many drives (both storage and optical) you have, but I'd recommend looking at reviews of a specific graphics card, 'cause they'll generally comment on the kind of power it needs.

Everything connects to the motherboard at some point, yes.

There's nowhere I can't reach.