First, you need to state your PSU spec. Pay attention to the +12V rail, especially for 8800GTS 320 you'll need at least 26A, recomended over 30A. For 8800GTS, your processor might be bottlenecking the vga. I think 8600 won't have problem but state your spec in more detail then maybe someone can help you.
The most important thing when you want to upgrade your vga is pay attention to your PSU specification. For 8800GTS 320Mb, your PSU +12V rail must at least has a total 26A, over is better. What is the brand and type of your PSU? What is the total amperage of your PSU +12V rail? You can look for it at the label of your PSU.
Again, I'm repeating my previous post, for 8800GTS it seems that your P4 3 Ghz processor will bottleneck the vga, at least you should using a C2Duo processor but for 8600GT I don't think so, you can keep your P4 processor.
Dont care about bottleneck issue because Game requirements change day by day that means your VGA card had to process harder for newer game due to complex special effects . For example Ouake 3 arena on a p4 3 GHz with Geforce 8800 GTS then there will be a processor bottleneck issue but if you play crysis with the same spec then the VGA card will bottlenecked.
People, I really get annoyed with all the "bottleneck" crap people keep posting..."your processor is going to bottleneck that video card, don't get it".
If that statement has any relevance at all, you would never upgrade anything because there is ALWAYS A BOTTLENECK SOMEWHERE IN EVERY SYSTEM. The video card may not live up to full potential, but it will be still be a big improvement over what he has.
Who is to say that he may be electing at this time to upgrade to beefy video card, and later as he has extra cash, he can upgrade other components later, like his processor? This is a very smart move as you get a lot more benefit with the fast video card not so fast CPU, instead of an aging old slow video card with a shiny new processor.
The CPU bottlenecking is absolutly true and should be taken into consideration. An 8800 is not a cheap card and unless you plan on upgrading the rest of your system very soon also a P4 will kill it's performance. I know this for a fact because I tested my main system (in my sig -the G92) and my other PC (Pentium D 820, which is better then your P4) and despite the fact that the Pentium system has more and faster ram it was no where even close to the other system with the better CPU. Unless you are going to upgrade the rest of your system within the next few months just get a cheaper card. Also a 8800GTS 320 is kind of a waste of money regardless the rest of your system. 8800GT(s) are much better for the money.