The cheapest way to upgrade would be to find out if your motherboard (likely an AM2 one, from the looks of things) can support the new AM3 chips with a BIOS upgrade.
Find out your motherboard model and manufacturer. You can use
this guide for this. Then check the manufacturer's website for a CPU Support List like
this one.
If any AM3 processors are listed along with a BIOS number, then you're in luck. You simply need to upgrade your BIOS to the appropriate revision specified in the CPU Support List for it to support one of the new AM3 CPUs like
this one. The motherboard manufacturer's support website usually has a link to the latest stable BIOS revision with instructions on how to perform the upgrade.
Be very careful, or have someone experienced do this for you; if done wrong, it can potentially ruin your BIOS chip and\or brick your motherboard.
The next thing would be to get some extra RAM (you probably have DDR2 [
confirm this via CPU-Z!], which is not commonplace, but not exactly very difficult to find either;
this one will do nicely, I think) and maybe a 64-bit copy of Windows 7, because the 32-bit version you have cannot utilize more than 4GB of video memory and RAM combined (essentially, some of your RAM will remain un-utilized). Of course, since you're on a budget, you might want to get this later since it can add significantly to the total cost.
Last thing would be to upgrade the video card and power supply; I'd recommend
this video card, although the power supply might be an issue if you have a pre-built OEM PC like a Dell or an HP. If you don't though,
this one will do nicely.
All in all, you can do this for around $300, I think.
Of course, all of the above assumes you can actually upgrade your CPU without getting a new motherboard et al.
In the event you can't, check out this build:
Others may likely have better input, so wait for the posts to come in before making a decision.
