I used an electric T50 to put the chicken wire on the frame for my run. I hammered a few poultry staples at the corners and middles, just for extra security, but the wire itself is flimsy enough that any outside attacker is just going to rip it away from the staples.
There a a couple of models of electric T50 - one that claims to be heavier duty than the other, comes with a blow-mold case and costs quite a bit more. Looking at them, it seems they both have the same internals, so I went for the cheaper one. It worked fine and I haven't killed it yet.
Use a lot of staples, and go back with a hammer and make sure they're seated. They don't always get punched down all the way, especially the longer staples. If you start at the middle of the panel and work your way to the edges you can get a neat and tidy look. Don't be afraid to pull on the mesh to tighten it up as you go -- it will look much better if it's not saggy.