I have built a similar size coop, and 3 by 3 is awfully small. I would build it at least 4 by 4. Then you can also take full advantage of the sheets of plywood that come in 4 by 8 size. I would also make the run bigger--banties may be small, but they still like to move around. I would make it at least 4 by 10, and cover part or all of it if you can. You will not regret making it bigger! I used 2 by 2 for the framing for my "cooplet" (only the base was 2 by 4) and it is plenty sturdy, make sure and put in ventilation at the edge. The height is a bit more than I did so that should be fine. I am building a stand, so that mine is off the ground at least 2'. Otherwise--everything that Pat said....
