I started using mercurial via bitbucket also, it's a really great service. We do the following:
For browsing, in the repository directory, the
hg serve command will serve you up the repo on port 8000 by default. That gives you the web interface/search/code highlighting, On my Windows PC I can then do
hg clone and I've got a backup of the repo. That's for free all built in to mercurial, you can enable an unauthenticated push but that's not on by default and I've not used it (see URL). The other nice thing is that it's only serving when you have the
serve command running. Repo is on linux so the push is handled by ssh which we have integrated with Active Directory at work.
See this URL for some push solutions: