The latest version of Qt is 4.4.0. If you get the commercial version, then it integrates very well with Visual Studio 2005/2008. If you use the open source version, then you will have to build Qt yourself (not too difficult), and the integration is less. If you are not using the commercial version, then you can still use QDevelop or Eclipse as on IDE.

To make sure Qt builds on all platforms, use Qt's classes whenever possible, even for low level stuff like files and sockets. Use qmake project files (in Visual Studio integration, you can import/export .pro files).