I'm using masonite as the backer board here for the window picture frame. It's thin and stiff and will work fine, so will cardboard, foam board, or any other thin material you'd like to back your photo with.
I cut it down to the exact interior dimension of the window on the table saw. The matte was professionally cut at a craft store so that it would fit in place snugly. Michael's cuts mattes for not too much money, as will any other framing shop as well.
If you're going to do a bunch of framing, I highly recommend investing in a matte cutter
that you can use at home. Cutting your own mattes saves a lot of money, is way more convenient, and allows you to make any size matte you like! My Dad has one and it has paid for itself many times over on framing projects.