First of all I was wondering if I should use Qt and Windows together. If so should I use VC++ 6.0 IDE or another one?
They work pretty well together.
I have used Visual Studio Express 2008.
I'm of the opinion that no one should be using VC++ 6.0 for anything at this point. Your better off just getting the express version of 2008 if your worried about cost.
I work on a product called ParaViewGeo (paraviewgeo.mirarco.org). It makes extensive use of Qt and we have been successful using Visual Studio 6 through to 2008.
Since Qt is cross-platform, I'll go tangential here and mention that another good cross-platform idea is CMake which is a cross-platform Make that can generate Visual Studio solution files from your code, as well as project files for other compilers, in case you do change your mind and get a different IDE.
There's also Eclipse which is free, cross-platform and has a ton of plug-ins.
Check out QT Creator
Qt® Creator is a new, lightweight, cross-platform integrated development environment (IDE) designed to make development with the Qt application framework even faster and easier.
Tailored specifically to the needs of Qt developers creating cross-platform applications Focuses on features that boost developer productivity without getting in their way Helps new Qt developers get up and running faster Open and extendable; integrates familiar tools and file formats
The final release of Qt Creator is planned for early 2009.