Well first off, i hope i am not out of line here, the 3-12 pitch isnt alot so i would go with PT 8"X8"s for you supports. You should use a TJI layed on its side for the top plate. Then you want to fill the void of the TJI with LVL's for you top beam. For you rafters i would use TJI's 6"OC to carry any kind of snow load. Now with proper clamping and use of glue you wont need any screws or lags, you would want to just tack everything together until the glue sets. For tieing into the main roof just fire up a saw and cut holes in the roof to allow the TJI's to slip inside but you want to use alot of caulk to prevent any leaks. What are doing for the shingles or tin? I would place tin sideways so any water runoff from the main roof would slow down on the shed, er i mean deck roof or else the water runoff will shoot right off the roof. I hope i have been of some help, lets be safe.