When it comes to graphical tools for git, the only useful tool I've used so far is gitk (which visualizes the revision tree for you) and I've been using git for the past half year myself, As someone else here put it, TortoiseGit is still very early and has some kinks to work out.
At work we've been evaluating three different DVCS's (namely git, mercurial (hg) and bazaar) and had a full packed evening presenting them for the rest of the company. Mercurial received most positive response and there is a Tortoise variant of it.
I'd suggest you do the same thing. Find someone who can present some alternative to git (such as mercurial or bazaar) and do a presentation together on DVCS at your company. It is more important to tell your coworkers how awesome DVCS is rather than the boss because in the end they will be using it. So it's more educational if they have been exposed to such tools and get a taste of it for themselves.
When we presented it we also assumed people didn't do version control so we explained quickly basic concepts such as checkin-checkout vs. commit-merge and why people version control. Basically it was like Eric Sink's articles on version control but stripped down to bare essentials.
Since you're going from VSS (and I'm so sorry) you might want to have a look at SVN. However as I see it, the only difference between distributed and the centralized approach is the added complexity of sharing code through a peer-to-peer looking network.