In my case it's an 8600 GT with 256 MB RAM
Well, just to be honest: I'm not very technical about hardware and stuff, but these are just my own experiences, etc. and for games of this generation, 512MB VRAM has become a minimum if you want to be able to run the games at a decent FPS.
AMD Athlon(tm) 64 X2 Dual Core Processor 4400+, MMX, 3DNow (2 CPUs), ~2.3GHz
Your CPU isn't that bad, but you have to remember, what me and ForkTong mentoined, that games like this are very CPU intensive and will more likely require a higher-end CPU than a GPU (though doesn't mean a good GPU isn't recommended too), you could (at own risk, only if you actually know what you're doing, this could kill your CPU if done wrong) overclock your CPU to see if it improves your FPS at all.
In your case I personally think you would benefit more from a GPU upgrade than a CPU upgrade (at least, if you manage to overclock your CPU a bit so you can get it on par).
Ofcourse, all the things I'm saying are just recommendations, I don't know what you can afford and stuff, but with your current hardware I'm afraid you'll have alot of trouble running this game properly, if you can run it at all.
Genky: you're right, but I'd still recommend higher GPU's than nVidia 8 series and ATi HD3000 series.
Those 2 gens were the very minimum that I recommended, since those were kinda the first 'real' high-end GPU's back in the time when they were still new.
EDIT:
Oh and a question from me to you ForkTong:
Do you think I would get a major improvement if I upgrade from my current CPU, an AMD Phenom 2.2GHz (OCed @ 2.6GHz), the weakest type of X4 Phenom, to a Phenom II 3.4GHz (stock speed, will probably OC to to around 3.9), with my other hardware being 4GB DDR2 RAM and an ATI HD4870 1GB GDDR5?
Since right now I'm running on Medium with a rocksolid FPS of 60 (almost) all the time, though once I change the settings to High it drops all the way to 25-35.
Because I was going to upgrade to that with Christmas.