Gotta add my two cents...
I'm a carpenter with almost twenty years experience. Staples will do just fine. I used em on my run. Now, I don't like the look of wire stapled to 2x2's, so I covered the boards with some cedar for appearance like Welasharon.
It is true that staples will pull out of wood more easily than screws, but I seriously doubt any predator will be able to pull out those staples. I did some searching on an engineering site I use for projects, and found that a 16 gauge staple penetrating only 1/2" has 84 pounds of withdraw strength. A staple penetrating 3/4" has 151 pounds of withdraw strength. 15 gauge staples at 3/4" have 174 pounds of withdraw strength. You're using 1", so think of how much YOU have, even with a lighter gauge. How many raccoons or foxes can pull with that kind of strength? And that is just one staple, with a staple every three or four inches, well, the wire will break long before those staples come out. Nailing a strip of wood OVER the wire and staples will help prevent the wire breaking.
Hope this helps.