HP is usually one of the more unreliable brands...I'd avoid them. The highest quality desktops I've seen from a major brand would be from Asus, though they can be hard to find.
The most reliable unit would be one that you build yourself, since you can pick reliable components. It's also often cheaper, since you can pick only the parts you need. This is what most everyone on the forum would recommend, and it's quite easy to do. Failing that paying a company to assemble one from parts you pick would be the next best option. I think Suuperbiiz will do it for $50.
The best place to buy is Newegg.com, but there are a few other good ones as well. (like superbiiz)
What is your budget?