If you are going to use Windows 7 with 512MB RAM, choose a 32-bit version.
Choosing Home Premium, Professional or Ultra won't affect memory usage, but Home Premium probably has everything you need.
You will get a lot of paging and slow performance on 512MB RAM. Windows XP will be better, but 512MB isn't great with XP either. You really need 2GB RAM with Windows for it to run well and be able to run most programs on it.