I have worked with computers for the past 12 years and have a few of my own. I can help you out with some input on what might or might not be a good deal. Try sending me an e-mail so we can chat somemore.
To answer some comments you have...HP is a strong brand name that has it's share of ups and downs. For example, I bought my wife a $1200 notebook (zv5200US) back in July 2004 for her school work. Two months ago the battery pack started heating up a great deal and the power cord got so hot that it burned my fingers. After contacting HP customer care, they decided to replace the entire notebook with a new model (zt8000) which came with a more powerful processor (Intel 640 with HT), a 17" widescreen monitor, opposed to the 15.4" we had with the old one, a DVD R/W Dual Layer drive, an extra 1GB of ram and a number of other upgrades. They did this since they considered it a "safety" issue and out of customer service. I have had quite a few different HP products over the past 10 years and some of them broke down...face it, it happens. However, one important thing you need to ask is, how does a company react with things go bad? HP and Gateway have been at the top of list for several years. I own 3 gateway desktops at home, 1 HP notebook, and 1 Dell at work. Out of all of them my Gateway 835GM desktop and HP zt8000 notebook are my favorites, I don't care for the Dell nor the current lack of service I have had from them. As for the Gateway, they will help you out over the phone for the life of your product, HP requires an extended warrenty or a fee to help you after your 1 year warrenty expires.
Walmart has a good return policy, but here is a little less known fact, Costco allows you to return your computer for any reason within 6 months of purchase....6 months!!! I don't know of anywhere else with a policy like that.
If you are getting the PC for your little one, the $300-$400 range is good, but you should expect to replace it within 18-24 months. This is due to the move towards 64 bit systems and software that will run on that. Further, you will need to look into a good size hard drive for the MP3 (music) and other media that your "pre-teen" will look into. If you could afford to go up towards $600, you could look at getting a Pent 4 2.8GZ with about 512MB ram, at least a 150GB harddrive, 15" flat screen monitor, DVD-R/W drive and a decent graphics card (look for a graphics card that has it's OWN MEMORY, NOT SHARED).
Hope this helps.