I am looking for suggestions for a git integration with VS 2010/2012 that allow developers use the basic operations (commit, push,pull,switch branches, tagging)
There are several:
1 and 2 gives you deep integration with the source control UI of Visual Studio, like padlock icons on files:
1 uses the ordinary Pending Changes tab, but adds some functions, like Switch Branch:
2 surely represents the future of Git integration in Visual Studio since Microsoft is behind it.
Note that 2 requires Visual Studio 2012 (with update 2 even), so if VS2010 support is a requirement you cannot use it. 2 is built into Visual Studio 2013
However, it sounds like you might prefer 3. Git Extensions is simpler and just gives you a simple toolbar with commit, pull, push, stash (not switch branch, though):