ATI cards have been doing fine with games for the last couple of years now. I'm only recommending ATI in this instance because the comparably priced Nvidia cards don't match the performance of a Radeon 9600 Pro.
Upgrading your processor is a good idea, but if you want AMD, you must change the motherboard out. If that's the case, you might as well go to an Athlon 64 since they're not much more than a good Athlon XP these days. I don't think that's wise, either, since you have a good motherboard.
Celerons don't perform as well comparatively to other CPU's, so it isn't a bad idea to look at another CPU. According to Abit's site, you can put a Prescott P4 on that motherboard.
http://www.newegg.com/app/ViewProductDesc.asp?description=19-116-171&depa=1
There are higher GHz variants of that CPU, but that's what you could do as long as your RAM is PC3200.
In your particular situation if you upgrade the CPU now, I don't see any reason to spend all that money for a motherboard, CPU, and fan when the P4 CPU's perform very well in games, and they fit your motherboard. Athlon 64's have slight edges in performance, but that P4 will outperform any Athlon XP (aside from insanely overclocked ones), and come close to Athlon 64's in games. Factor in you spend zilch on the mobo because yours will work great, it's a no brainer.
Mitch is wrong about the priority of what to upgrade. You'll gain more in performance upgrading your video card first if you're wanting better game performance. However, you should decide how soon you will upgrade your CPU. If it's any more than a year, just get the ATI 9600 Pro and be done with it, and buy a new video card when you replace the whole motherboard, CPU, and Fan later. Particularly if you plan on upgrading the CPU very soon as in the next six months, it would be wise to go ahead and invest in a higher performance video card, such as the Nvidia 6600GT.
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