The Aviary I am building right now is 16x20x9 and the attached coop is 8x10x8. In this project I have about $800. in Lumber, avaiary does not have a wood floor ( the aviary is set up so down the road I can add a floor metal roof and siding and I'll have a nice size garage, I could fit a car or tractor and other stuff no problem ) I framed it with 2X8 lumber for upper and lower frame, and I also used 2x6 and 2x4, the reason I framed it heavy is beacuase I framed it like you would a pole barn, You use less Lumber but should be heaveier lumber, If I was to side the Aviary it self I would ad a few more supports, The coop part is getting board and batten like the rest of the out buildings, My friend owns a large saw mill business so I can't comment on the board and batten since I get it for free most of the time.
16x20 Is a nice size, Bigger is always better, 12x12 would make a nice garden shed, Of course if it just a garden shed you could o a touch smaller.