Blue29, the important thing to consider here is what you've stated to be your reasons for having a computer - music, games, internet!
The fact that you want games dictates that you need a Windows PC. Forget Mac, forget Linux. Although some games are available for those platforms, the mainstream of PC Gaming is Windows.
I'd also advise against buying a 'Name Brand' PC for one simple reason - you'll pay more for less performance! PC games are pretty much the most demanding task that you can use a PC for, and they require high performing machines. If your budget stretches to it, try to get hold of an Athlon64 system, with at least 512Mb or preferably 1Gb of RAM installed, either a Radeon9600XT or GeForceFX5900XT display card as a minimum, or preferably a Radeon 9800 Pro, GeForce FX5950 or better.
You're best to purchase a 'White Box' PC - one that's been assembled by a local PC supplier - or purchase the components and assemble it yourself. You'll get nothing more than an OEM copy of Windows XP and the basic warranty on components with your system, but the savings on all that Support and Service will enable you to have a better performing system for your money.
Oh yes! And don't forget to ensure you have lots and lots of hard drive storage space.