The Central Processing Unit: Gaming desktops need a powerful processor in their configuration in order to keep up with the ever-increasing requirements modern games have. Without a good CPU, you won't be able to even start-up such a game, not to mention run it. Your focus here is somewhere in the quad-core range. These can be a bit pricey, but they're a well worth investment in your future as a gamer, since they won't grow obsolete for years to come. Try to allocate at least 35% of your budget to this spec, since it's very important both for gaming and for other daily tasks you might run into.
You might also want to take note of the current socket your computer has for the processor, and explore upgrade options for that particular socket. But if you want a complete system upgrade, you'll also have to get a new motherboard to support the newer processor types that come out.
The System Memory: A decent amount of RAM will run a decent game. A higher amount of system memory will be a lot better for your gaming needs, since most games today require at least 2GB of RAM to run properly. If you really want to get the best performance out of your gaming desktop, your configuration for this spec should be in the 4-8GB RAM range. Luckily, RAM is an easily upgradeable spec, since most motherboards will carry around 4 sockets. If all the sockets are occupied on your system, you should look for RAM modules with a larger amount of system memory available.
The Visuals: The graphics card is the most important spec when figuring out the configuration of your gaming desktop. This is the element that brings true visual bliss to the gaming experience, so the joy factor will suffer if you neglect this aspect. There are tons of cards out there, but only a few which you can truly call the best. Since the best cards come at quite a big price tag, don't overdo it when purchasing a video card for your system. You should wait for a while since the prices on these things tend to go on a downward slope quite quickly, and you could get the same card at half the price in a matter of months, or weeks even in some cases.