For a new comp, I would choose Dell over HP. But I would suggest you or someone else you know build a computer for a fraction of that price. Do you want it to game or just surf the net? If your not planning on playing the more graphic intense games I suggest you save ur money and get a amd athalon 64 3200+ system, they are very cheap and reliable.
For fast internest...that's up to your type of internet connection. Get off dial up and sign up for DSL or Cable.