RE: Back yard bow range...
Congratulations on the new house.
Buddy you’ve got to be very careful. You mentioned that there are woods behind your house. How far do the woods go back and what’s on the other side of them?
As for a back stop consider this; buy three 4x8 sheets of plywood. One will act as the back stop, one will be the roof, and the third one will be cut in half and used for the sides. Use 2x4 too frame it and screw the top, sides and back together with 3 inch galvanized screws.
Stack square bails of straw inside. The roof will help keep the straw from weathering. Buy a block target and your set. This will cost a little money but Safety is #1 as always. That’s a small space to be working with so be careful.