I'd like it to be able to play Guild Wars 2 and Diablo 3 reasonably well. I don't care if it's on high or low settings. I don't need mouse, keyboard or monitor, just the tower (+graphics card, if necessary) for about $600. I also need it to support dual monitors.
I know the NVIDIA GeForce GT620 is not a great card, but could possibly upgrade it later. I also have the NVIDIA GeForce 8600 GT that's installed in this computer that I could use, but not sure how the form factor will affect that (or if that card is any better, which it probably is not).
My preference is for a prefab build I can slot a graphics card into, but I'm not opposed to building my own as long as it is not hard to assemble (screwdrivers ok, soldering not ok). If I go this way I'm likely to need specific links to components to purchase.
The computer I have now runs both games but just barely. To give an idea of what I'm working with now:
Pentium D 3.00 GHz
2 GB RAM
Windows 7 64 bit
NVIDIA GeForce 8600 GT
Obviously I'd like the new system to be significantly better than what I'm currently using.
I bought mine a few years back and splurged a lot more than you're planning on, but I'd suggest looking at a small SSD as well - have the OS installed on that, and it will start up notably faster. It may not seem like much, but for something you probably do every day it's a really nice little touch. I haven't priced them lately, but I bet they're cheaper now than when I bought my pc (was pretty expensive then).
(Just doing a quick search, it looks like you can get a 120 GB one for ~100 dollars. I haven't checked, but I think windows 7 is only ~20 GB, so this would also leave you space for games if you wanted to help them load things faster as well... you could probably find a 64 GB one somewhere just for the OS even cheaper.) Then get a dirt cheap hard drive - or just take the one from your existing PC - and save all your mp3s, documents, downloads, etc there. It takes a little bit of legwork to change the default download/save folders from the SSD you put windows on to the other hard drive, but it's nothing that a good session of googling (or two) can't handle. Between the two drives, you'll have more space than you know what to do with.
The SSD I bought was way less than 120 GB, fyi, so if you want to save cash go for a smaller one. I don't think I even got the 64 GB one (I feel like they've really come down in price... almost a steal now. Kind of a luxury bit then).
If you need to cut money.... I'd opt to cut it on the graphics card rather than skipping the SSD. Getting a new graphics card in the future is pretty easy, and you'll probably be able to buy a better one for much less than it's currently selling. Getting an SSD in the future, deleting your OS, reinstalling the OS on your new SSD and setting up the PC to boot from it... I'm sure it's not /that/ hard or anything, but I wouldn't want to deal with it. Just make sure you're 100% positive the card you get will run the games you like on at least medium+ settings.
Anyways, this is just something you might want to consider. I like my SSD a ton and would definitely get it again if I was buying a new PC.
Edit: I'm sure the amazon links you were given above are great. If you want to do some more browsing for a build it yourself PC (of the screwdriver variety), you could check out http://www.newegg.com too. I got mine from them. I wouldn't give it a 5 star rating (I got pressured into getting a pricier graphics card to avoid a shipping delay.... but I didn't /really/ mind since I'd wanted an excuse for the good one anyways...), but it's a legit site with some good deals on electronic parts.
You don't seem to be after a fancy gaming PC, but I've heard good things about http://www.falcon-nw.com/ as well (although I've never bought one there). Apparently they have a stated policy of not voiding your warranty if you do things like overclocking, which is a pretty cool company policy imo.
Hope any of this was mildly helpful. Have fun buying your PC - I always feel like a kid on christmas when I get a new pc.