I think to be on the safe side:
1. remove IExplore with this little IEradicator program
2. Get a printout of the r1ddler's secret files article and follow the instructions step by step
3. get Opera, or Mozilla or whatever else.
This way, even if the hidden files are still kicking around after step 1, step 2 will sort them out and no mistake.
I recommend Opera. On windows (but not on Mac) it has that excellent thing that IanC mentions where you only get 1 window, but each new window opens in a "tab", if you've ever used M$ Word (shudder), then you are familiar with this idea.
Haven't tried Lynx or Mozilla yet, but it might be worth getting them in addition to Opera, since as Karen says, the free version of Opera has a banner ad in the toolbar, which can get a bit annoying, although it never bothered me much...
Opera saves a "mystery history" file too, but it is VERY easy to manage and VoidMain and a couple of others answer this query in another forum somewhere on here...