That's a crappy system. Seriously. Build your own, get the parts from reputable dealers on eBay. Do some research so you don't get burned.
And don't listen to KingofGnG. AMD is not garbage. AMD created the 64 bit CPU. Which is running on my ASUS Crosshair I motherboard (Republic of Gamers)
So seriously stick with an ASUS or Gigabye motherboard, they make the best and use the best parts in the manufacturing. Especially the capacitors (yeah it DOES matter).
Use EVGA or XFX for videocards (RIP BFG). Use Corsair or OCZ for memory. Use Thermaltake or Corsair for power supplies (though do some research). And it's up to you if you go with an Intel setup (READ limited upgradability) or Advanced Micro Devices (extended upgradability on existing parts).
I've built well over 17 computers since 1994 and through trial and error realized buying cheap costs more in the end.

Well that says it all, doesn't it? "I prefer Brand A regardless of the fact that I know full well that Brand B is better right now." Congratulations on invalidating your opinion utterly.

Tell me about it. I think I have been changing a PSU on my old desktop every 9 months for the last six or seven years, or something like that. This will be the last time I'm buying something cheap because I don't have a "need" for something better. If it goes bye bye once more, then its time for something more expensive.

I won't argue about things I haven't the time to deal with. NVIDIA > ATI for me, end of the story.

AMD aren't garbage and put out solid graphics cards (my lower end HD3650 still does a good job on newer titles), on the cpu side it's been a while since they were king though they still put out solid stuff. They were the toast of the cpu town when their X2 dual core smoked intel's first gen dual core but intel has crushed AMD in overall performance since the intel core 2 came out.

If you don't have the time to actually substantiate your argument then don't bother at all. That way you'll save even more time.

For me personally I've preferred nVidia because of the issues I've always had with ATI cards. Granted it's always a driver issue, but still.

ATI's drivers are shit. They always have been, and no matter what some people profess, they still are. They've got some amazingly skilled people working on the hardware and some work experience kids working on the drivers - who are probably hoping it will help them get their GCSE in IT.
There's also the fact that ATI is very poorly supported. If a game has any problem with either Nvidia or ATI GPUs it's invariably ATI cards that have been neglected.
The fact that their management has a major stick up their arse doesn't help either. Yeah, not including PhysX support because it's Nvidia branded is a real way to win customer loyalty, isn't it? Morons.
Comparatively Nvidia are just average. None of the highs, but also none of the lows. Dependable but not spectacular. Personally, right now I'm far happier with that than trying to find ATI drivers that are so old they actually work. Especially considering we seem to be faced with at least another couple of years of the current generation of consoles retarding graphics development.

Show me where anyone claims this is ATI's fault? From what most rumors say Nvidia isn't willing to support ATI cards unless ATI pays them more than physx cost them in the first place. Ask Nvidia why physx for CPU is coded with x87 not SSE instructions or why its limited to a single thread. Nvidia deliberately limits physx support to their cards only.

OK, so what is about the best computer I could get for under $300? And preferably closer to $200. And I'm talking used parts, throwing stuff together kinda computer. What are the things I absolutely can't scrimp on, and what are the things it doesn't matter overly much?
Basically what's the best computer I could acquire (In any way, be it custom built, off ebay, combination of both etc. ;) for around $200?

I really like catalyst control center. It's nicer then the one i remember from nVidia. Apart from that, drivers do have compatibility issues but nothing that would ruin gaming experience. All in all i'm really happy with my ATI gaming computer and it's performance. Especially considering it didn't cost me a fortune to put it together.

Apart from the fact that Nvidia were going to employ the guy to officially produce ATI PhysX drivers. That's not the attitude of a company that wants to exclude AMD.
Yes, AMD aren't going to support a competitor's product. Even when it's of benefit to them and their customers to do so. But that's the problem, not the answer.
PhysX is widely supported by developers and considering it doesn't degenerate into the stretched spindle dance-fest that almost every Havok game I own has done, that can only be a good thing.

I made the switch to Nvidia not so very long ago and they're pretty much the same now, in terms of features. CCC has a nicer interface though. But when AMD insist on throwing out monthly driver updates that get progressively worse and worse. Well, that's why I switched.

of course nvidia wants ati to support their product. it will make amd graphics department depended on nvidia...
Market penetration baby. Make ati cards support physx. More games support physx. More games support physx, greater control over the market by Nvidia.
and then cut ati off.
when over 80% of games are using physx.
You see how your argument about physx is illogical now?
Furthermore: Recent Nvidia driver update burned down cards... I choose a glitch over my computer turning into 'fireball' (exaggeration, metaphor)