The 12's are fine for the joists…even a little on the strong side (which is good). For the attachment to the house I would use some expansion bolts (it's basically a threaded rod, with a wedge on the end, some shims in the middle and a nut on the other end. when you tighten the nut it pulls the wedge into the shims and makes it's own anchor; these are MUCH stronger than tapcons, which aren't really structural at all). You'll want to put two anchors a foot in from each end, and then stagger one every two feet (3 inches from top, 3 inches from bottom etc). To clear span the 20' on the outer edge you'll have to use a treated glu-lam beam, at least a 6.75" x 16.5" beam (this is the minimum, number from Boise lumber). One each end you'll probably want to use 8×8's with a slight taper two feet from the top, then the top foot plumb again at 6.75", you can get a special metal connector from USP that is a post to beam in galvanized steel to connect the two. OR you can use 8×10 posts with 6.5" cut out of the top to make a ledge for the beam and through bolt the beam and post with 1/2" carriage bolts. You could get away with 6×6's and a 3.5" thick mortise and tenon into the beam as long as it is 6" long. To make everything cleaner looking, use hangers on the outside as well and hang the joists from the side of the beam. I would encourage you to place rubber on top of the glulam to help prevent water from sitting there and promoting decay. I'd encourage you to put 1/4" spacers between your ledger board and the brick to let water drain through and not decay the ledger board. If you have any other questions feel free to ask! (I've done this for awhile…)