I had XP 64 and hated it because it was hard to find drivers sometimes and games actually ran slower than on 32 bit XP, and some would not even install because they didn't recognise my O/S. XP 64 wasn't even detected properly as HDCP compatable and I couldn't play blu-rays. I have had no such issues with windows 7 64 bit. Go for 64 bit, Windows 7 is made for it, unlike XP.
Some older games may not work on new OS's like Win7.
Games would work good on 64-bits as well. Although some games may have some troubles.
If upgrading the RAM, to more than 4GB or so, 64-bit is recommended.
64-bit is fine for newer games these days. Also, games are only going to need more system resources as time goes in so a 64-bit system will let you add more RAM. It's not a major consideration, but it's an easy way to avoid a potential future bottleneck.