A good computer name is hard to find. Compaq, even though a big name in personal computers, make terrible products(ok, there business line is ok, the presarios are crud).
I happened to own 3 e-machines (ranging in age, from when the first came out around 4 years ago, till one i got 3 months ago) and i have yet to have a problem with any of them. These machines are reasonably equipped for under $500 US.
The best thing to do is go to some stores, pump the sales guys for information, but leave your wallet in the car. After you've learned all you can from the different sales guys at all the computer stores, then you start "price shopping" and picking out what you need in a computer. Then you can simply go to ANY store that sells the computer, and get it without hassles from the sale's guy. There is nothing more frustrating then getting all hyped up by a sales rep, shelling out tons of cash, and you get a lemon.
Its a crap shoot, and I wish you luck.