Most ATX power supplies fit most cases. With one exception (the Antec CP series, which is significantly bigger), most power supplies are the same width and height. The depth/length is the dimension to check - it's how far the power supply extends from the back panel into the case. Some high-power power supplies are extra deep, and won't fit into tight spaces. This is particularly true of cases where the power supply sits opposite the 5.25" drive bays, and the case as a whole is not too deep. In cases where the power supply is mounted at the bottom you generally have more room. You also want to check on the orientation of the power supply fan, although most modern cases have been designed to allow for a fan on the bottom of the power supply - the days of discovering that your case insists on mounting the power supply with its fan against the top or bottom of the case should be long gone.
ATX12V was a revision to the original ATX power supply. The ATX12V 2.0 version was introduced in 2004, so you shouldn't find anything earlier. I'd expect most power supplies to be ATX12V v2.3, given that version came out in 2007.
Many motherboards today use an 8pin connector for additional 12V power, rather than the 4pin used in ATX12V. Sometimes this is labelled EPS12V.