You can likely get it pretty clean with Add/Remove, but uninstallers rarely remove all of what they've put in the registry. (Registry cleaning is a cross between voodoo, black art, and placebo.) The best thing to do wipe the new computer and put a fresh install of Windows onto it, but HP/Compaq may not give you a "just the Windows, ma'am" install disc (set) with the computer.
Also, there probably exist numerous sites on the internet with instructions on how to get retail PCs to a fairly clean state.
As always, if you have specific questions after you get your new toy/tool, fire away here.
