What are the benefits and disadvantage of using either Git Extensions or TortoiseGit on a Windows Based OS?
I can't speak to Git Extensions as I've never used it. Had some problems with pure GIT. Couldn't integrate GVIM, for instance. Tortoise Git has an integrated editor and diff tool (which is amazing), so that's a very nice convenience. I loved the branch diagrams in the Scott Chacon book and was hoping TGit would have a similar diagram. They do have a tool for showing branches but it's not as nice as the one in the book.
One thing to bear in mind is that since TGit is just a shell on top of GIT, there's no harm in mixing the two methods. I use TGit for most everything, but dip into GIT for commands that are awkward or that I simply don't understand well in TGit. But even if you plan to use TGit, it's still important, as mentioned above, to understand the basics of GIT first. I'd read through the first, say, three chapters in the Chacon book (available for free online at http://progit.org/book/ or by purchase at Amazon). If you're like me you may want to read them several times over to let the paradigm sink in. It's not all that complicated, but it is very different from previous VCS's.
TGit never crashed on me, as it has for some of the other reviewers, but then my repo's have been small. It did eat my commit comments on more than one occasion, which could have been user error. Since you can go back and re-edit comments this was just an annoyance and worth the convenience of having a GUI, with windows that show a great deal of info at a glance.