My first thought was, wow those are big timbers, what kind of weight will it be holding? Are you in snow country? If not, 2 x 6's or 2 x 8's should be fine with a 4/12 pitch on the roof (depending on the style of your home, you shouldn't need 2 x 12's. I would remove the stucco and insulation board, you will need to get flashing underneath the siding and have it sit on top of the new roof for water runoff.