Do a full directory backup/archive. It's a little easier if you are using cpanel. You may need to do some tweaking in respect to the path settings and database names/paths, etc if you are restoring to a different hosting account.
I would like for the info to be updated across both domains as users are using the site, this way if one goes down there is still a working site available.
never mirrored, but I would do it by, using different servers and placing different dns to the servers im using and just upload whatever to all servers.. thats if, what im updating doesnt take forever
PS - just back your server up a few times a day, mirroring isn't really for back-ups. Redundant servers will be very expensive, twice the cost for the servers, plus the cost of making them talk to each other, etc.