Your area/region may come into play as in what type of animals you've got about you. If in town or country sort of thing. In towns your really only keeping out dogs and skunks, few others maybe but loose dogs is a big thing.
Electric poultry netting is a really good option but then if your in a heavy winter area it may not be used all year. If it can be used all year that's my favorite. We use 164' of 4ft poultry netting, 4 extra heavy duty posts to aid in keeping tight with hotgate and P5 charger. Makes for over 40x40 run that's portable and cost all told $350 range. We went with the P5 as it can be moved far away from outlets and run off battery. Big area to move around on.
In general the coop is your biggest protection and to work must be locked up every night. That takes care of a lot of predator problems right there. Coops get all holes/vents covered with 1/2 inch hardware cloth. The run itself can be covered with 2x4 welded wire. Smaller and square looks nice but hard to find and bit pricey. 2x4 14 gauge is $36 a 4x50 roll at your area box store like Lowes. Cover the top of run too. Without electric critters climb so a top is needed. Think raccoon. Many digging predators and in towns your biggest problem will be skunks. Large skunks do indeed dig right under the run wall and kill birds. An apron stops all that. I use the same 2x4 welded wire and cut lengths then in half. 18-24 inches flat out from run wall is all it needs to be. Either stake it of lift sod and lay sod on top of it. Two side are cut longer to make a complete perimeter. Again, without electric many animals dig under.