The windows-7 web site has a comparison chart of the different capabilities:
http://www.microsoft.com/windows/windows-7/compare/default.aspx
I think the home premium version will be suitable, unless there is a feature that you really need. Note that XP compatibility(present on all versions) is different from XP mode which requires professional or ultimate. It allows you to run XP in a virtual machine and is not suitable for gaming.
Almost anything will run under the 64 bit version that is required to be able to use all 4gb. There are very few exceptions, and most of those have a newer version that runs on a 64 bit OS.
Shopping tips for Vista:
1) Do you qualify for an academic license?
If so, you can get windows-7 at a discounted price(about $30).
2) Look for an upgrade version of home premium instead of OEM.
Upgrade is a retail version which gives you support from microsoft, unlike OEM(AKA system builder),
and allows a more hassel-free ability to transfer the os to a different pc(motherboard).
You get both 32 bit and 64 bit DVD's so you can dual boot with either version if you need to.
There is a legitimate two step instalation process to install an upgrade version
You install windows-7 from the cd, but do not initially enter the product code or activate.
After it installs, you have a fully functional OS for 30 days.
Step 2 is to insert the dvd again, while running Windows and then do an upgrade.
This time, enter your product code, and activate.
After activation. you may delete the initial version which is named windows.old.
If you get a retail or upgrade version, you will still be able to upgrade to ultimate later, not so with oem.