I don't understand that, so I'll just get the cheapest 500W power supply I can find. That should be OK, right? Also, do I need a new case or cooling system?
Highly recommended that you do NOT get the cheapest power supply you find. It would be much better to get a high quality 400W (for example) over getting a cheap 500W. Cheap power supplies have to be one of the top problems people have, and causes strange system failures from an unbalance power distribution.
Well then, to be safe I'll get the most expensive 600W power supply I find. But will the same old 3 fans and case meet my newly awesome system's requirements?
Depends. If your new motherboard is an ATX motherboard (which most SLI boards are, if not all...??), then you just have to be sure your case is also ATX capable.