You can download Qt SDK from here (the SDK come with Qt 4.7.0)

Or try Qt SDK tech preview, from here (this includes Qt 4.7.1 for desktop and mobile)

Or you can download the sources and build with what compiler you want, but the easiest for you is to get the SDK, since it installs everything.

The integration to Visual Studio or Eclipse makes sense only if you know the environment very well, else just use Qt Creator.