Unless you know a lot about this kind of thing, with lots of experience, I would go with a name brand PC, either new or refurbished. For example, Dell sells new and refurbished PCs on their website. Sometimes you can get a very good deal on a refurbished Dell, WITH a warranty.
A few years from now, when some critical part goes out, you can go on the Dell web site and find out exactly what was in there, so you can be sure of getting a compatible part.
Compaq puts a spare part number on EVERYTHING, and so if you match the spare part number, the part WILL work.
I've seen too many cases where the "no name" companies buy no-name junk parts for the PCs they sell, just to shave a few pennies off of their cost. What will you do when two years and one day have passed (i.e. the warranty has just expired), and your system board goes out, or your CPU needs replacing? Unless you are very savvy, you won't know for sure what will be compatible.
I know how this kind of thing works. Ihave seen lots of underhanded practices and outright lies on the part of some of these companies. (Not all, just some.)
I saw a case once where a friend of mine had purchased a computer with 8 megs of RAM (this was a while back!). He wanted to install more RAM. Guess what? There were 8 SIMM slots, and 8 1-MEG SIMMS installed! He either had to throw out some or all of the RAM he had, or he had to go back to the same guy he purchased the system from for a warranty upgrade!
I knew the guy who sold him the computer, and he was one of the kinds of dealers who would buy the cheapest junk he could find, to shave a few pennies off of his cost.