Hello, If I'm building a gaming rig, would it really be necessary to get windows 7 ultimate or is it going to be just as good with windows 7 home premium?
Premium will be fine.
Ultimate adds BitLocker (Hard drive encryption), support for Networking Domains, the ability to back up to somewhere on a different network... etc... None of these things are necessary (or even desired) for a gaming rig.
In addition to what Scott said, Ultimate also adds multiple language support and XP mode to run programs that doesn't have support in Win 7.
Also, Home Premium has 16GB memory limit (64 bit). Everything above, including PRO has much higher limits.
No gaming specific improvement in any of Win 7 versions.
The Pro version has all the Home Premium features plus: Ability to join a domain XP mode Network backups Remote desktop (all versions have the "client", but not all version can be connected TO)
The Ultimate version has all the Pro version features plus: Language pack support HDD encryption
I would also like to point out there are other programs/options if you decide you need X feature later on. For example, for remote desktop I've started using logmein, which is free. If you need to encrypt a harddrive I've heard many good things about TrueCrypt. The XP mode found in the higher versions don't allow for video acceleration so gaming isn't possible. You might be able to find a VM program that allows the same thing however. (virtualbox?) As you can see MS includes many extras in the higher version, but you can find similar (and free!) just by looking around.
Edit: Forgot to mention that I don't know of any other way to join a domain. If you need that functionality then you'll need the pro version. If this is a straight gaming build HP will be fine.
I'd go w/ pro .... especially when the cost difference between it and HP disappears in many of the newegg combos.