Do not buy an E-Machines. That is my advice. Find a small computer shop and see if they could build you something in a similar price range.
Here's Anandtech's article on entry level and budget PC's:
http://www.anandtech.com/guides/showdoc.aspx?i=3486
Both the AMD and Intel builds in the $538 category are much better than the E-Machines Celeron. The AMD has integrated ATI 780G graphics and the Intel has integrated Nvidia Geforce 7100. The AMD has better graphics, but Intel has a better entry level processor. When it comes to graphics, Intel's lousy, which is why the Intel entry level build has Nvidia integrated graphics instead.
How much is that E-Machines? Add to the cost a budget $50-75 video card (that's about all the power supply in an E-Machines of that class can handle). You'd also have to pay labor to install the card if you don't know how.
Really, look for a small computer shop and take printouts of the AMD and Intel builds with you and see what they can build in your price range. If you can go slightly higher to the $800 range, you can get a PC built in the same range as mine. I have virtually the same (or slightly better) than the article's AMD budget build (my year old last generation graphics card is equivalent to a 4850).
When I had to get the 3870x2 repaired in my system, I switched to the integrated HD 3200 780G graphics and it played Lord of the Rings: Mines of Moria at medium/high settings. A 780G would play WoW without any issues (and the Nvidia wouldn't be far behind if you went with the Intel build), so I definitely recommend avoiding the E-Machines Celeron and getting a custom build.
If you don't trust a computer shop, try to find a store like Fry's that can build it for you. Fry's is only in California, Arizona and Texas, but other big box PC and electronics stores might do the same if they also sell components like motherboards and CPU's. There are also reputable online custom builders, but since I build my own and buy components from Newegg or Fry's, I'm not up to speed on the online build recommendations.
Good luck and let us know what you decide.
Edited to add that I just checked out that E-Machines at Walmart online where it's $498. That definitely makes it a bad idea. Both the $538 entry level builds have it outclassed, and the $831 budget builds would allow you to be a bit more future proof for games and applications over the next 2-3 years.