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)
Visual Studio for Git with VS 2012, it's matured now (version 1.0).
I like deep integration with VS 2012 especially switch between branch seamlessly, you will work with any branch at any time.
Another thing is that it's working very well with Bitbucket.
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):