The single most important piece of advice that no-one seems to mention is this:
Get your wire first.
Most of your uprights and crossbeams etc will depend on the width of the wire. You can't fix wire to fresh air. Whatever the height of your coop/run, do it in frames. And make sure the center to center measurement of the upright is the same as the width of the wire. If you can, cut the timber together, ie, the top and bottom of a frame or the uprights. Once you've got the frame nailed together, make sure the corner to corner measurements are the same both ways. This will ensure they are "square". Then you can nail on your braces and it won't move after that.
Good luck.
Paul (I must get around to finishing my coop page which will also show the electric aerial that opens/closes the pop door)