don't write off cyberpowerpc, they make a hell of a gaming computer for a hell of a deal. you just have to know how to pick the parts.
the biggest mistake people make is getting top of the line cpu, gpu and ram and ignoring everything else. as mentioned, you're going to want a power supply that is more than 500w. don't skimp on the rest of the computer, or else those parts will throttle your gaming components.
and i don't know why you'd avoid something that says it's for gaming. that IS what you want to do with the computer...

Thanks for the responses and recommendations!
Well, I guess I need to read up on some things first.. The last time I bought a piece of computer equipment it was a Creative Labs SoundCard :)

It's not just the wattage, but the quality of the PSU. I'd much rather have a decent 650w unit than an unbranded 1000w unit any day.
What you're using the computer for isn't in any way affected by the case. It doesn't make it any more a gaming computer because you've bought a gaudy case for it.
You're going to want a good quality case that makes building and upgrading easy, reduces noise and generally is not going to last. Something which you will find in a Lian Li case. But not in a typical 'gamer' case. Which is usually comprised of plasticky crap.

i'll agree with you about the case. not only are they gaudy and inefficient, if you like the way gaming cases look, you've got some pretty terrible taste.
however navagon, you said 'any hardware with gaming in the description, other than gpus, and even then...'
i think it's an exaggeration that hardware labeled gaming should be avoided. sometime's it's used to sell something to gamers that is not actually in any way better for gaming than the alternative, but the gaming label doesn't mean something is worse. and it often is used appropriately--my gaming mouse can attest to that.

I'm not saying it's necessarily bad. Just usually very overpriced... and not very good. My experience with gaming mice began and ended with Razer. Below average is a nice way to describe them.

Cases often come down to personal taste. Antec's gamer cases are superb for cooling and certainly help with overclocking but I realise the metal mesh design is not for everyone.
As for the power supply Novagon is correct that its actually one of the most important components you can buy. A lot of people save a few bucks with a no name then run into stability issues because the current supplied is not stable. Enermax, Seasonic and Antec make quality stable power supplies. Zalman make heatpipe cooled PSU's that are expensive but worth it if noise is a concern. I personally use an OCZ (PC Power & Cooling) Mod X Stream 750w because the black case and blue LED fan complement the Antec 1200.
9800GT again as Novagon said is just an 8800GT with an extra chip that enable a useless feature called Hybrid SLI. If you want decent gaming on the cheap then you should look at the ATI 4870 1GB card. It can run pretty much anything up to Crysis and there is no point spending more at the moment given that DX11 cards are due soon.

I don't think the "system requirements" for a LOT of the games here on GOG are accurate anyhow. A lot of which are actually WAY lower than stated. For example, Duke Nukem Atomic Edition does NOT require a 1.8Ghz CPU and 1gb RAM etc. I remember playing Duke back on P1 systems. 3D realms recommends...
"486DX2/66 with 8 megabytes of memory and VGA graphics. We STRONGLY recommend a good Pentium with 16Mb of memory and PCI local bus video."
And that is taken directly from the 3D realms website.
As far as getting a new PC, you're generally better off building your own as opposed to buying a prebuilt PC. Just basically figure up the specs you are going to require for what you want to do (find a power hungry game you want to play), then find the parts. If you've got a little extra $$, buy a motherboard that can handle MORE than what you are putting in, to leave you room for upgrade in the future if needed. Also, if you buy parts online, here are a few places I like...
www.newegg.com - Overall parts and basically everything
www.xoxide.com - Mostly case modding supplies and some gaming stuff
www.frozencpu.com - A bit of everything
One last thing, however much RAM you think you need, double it. Don't forget that just because a game requires 512MB RAM and you have 512MB RAM, that you are fine, because some of that is already in use by loading the Operating System, and any other applications running in the background. I've seen insufficient ram kill off MANY hard drives, including my own in past experiences growing up. CLICK CLICK CRASH
Hope that helps a little.

I think it's because of the DOSBox wrapper that requires that additional specs...

That is exactly why, but GOG does use a general estimate for for that, since the DOSBox requirements vary depending on the game and system it is emulating:
http://www.dosbox.com/wiki/System_Requirements
By putting that 1.8GHz requirement on there, they are guaranteeing that anyone using a DOSBox-based game is at least able to emulate a Pentium 2, which should be enough to run any of those games they are currently offering.

True, I didn't think about the DOSbox