It has been found that the processor and the GPU of the first generation iPod touch is noticeably slower and inferior to the second generation iPod touch. There isn't really a list of games that do or do not work, just that the first generation iPod touch is less powerful; I have a first generation iPod touch, and games play fine. Certain hardware is not available on the iPod touch 1st gen like Bluetooth and such; there may be applications in the future that require such appliances, which would make them unusable on the iPod touch 1st gen.
As with the software itself, as far as I'm concerned I have iPhone OS 2.2 and everything works fine and dandy.
For future compatibility sake it would be a better idea to buy the second generation iPod touch simply because some hardware enhancements cannot be added with software updates to the iPod touch 1st generation.
I hope that answers your question.