I think that is a workable budget ... There are some prefab sheds on line that can be retro fitted to make fine coops and electric poultry netting that are relatively inexpensive to use as runs
So you have done the chicken math ....Now exactly what is a "shoestring " budget ? Am assuming you can to this site for realistic answers - if your talking about trying to do this project on say $100 dollars I hope ya'll are good at scrounging used materials