http://stackoverflow.com/questions/6011893/tortoisegit-vs-git-extensions
You want Git Extensions for one important reason - it shows you the graphical view of the commit log (see below). Without that graphical view I don't think most folks new to git will ever get what is going on with branches, commits, rebasing, cherry picking, etc (I know I didn't).
You are going to do want to do some of your work on the command line also, it's your best bet to practically use git since all the help you get will be command line based.
All that said, you can use Tortoise Git also (assuming it works) since they all call the same command line executables and act on the same git repository.
Most IDEs have git support also, JetBrains IDEA does a great job of adding change lists and other functionality on top of it.