Lenn, I would suggest using 2 x 6 joists and having them 24 inches OC.
I would also use a 2 x 6 or 2 x 8 ledger board against the house bolted on and then use joists hangers for the roof joists to hook up to.
4 x 4's would be sufficent for the beams and the spacing of the posts have allot to do with what will fall on your roof. Are you in a snow area?
Normally, I would think that 3 posts would be fine, but the snow and ice is another factor.
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