My cages are home built too, they can't get to any wood as the base/tray is made from coroplast and creates a barrier between them and the wood frame. Just be sure they can't get to the wood, mine even has a 2 inch gap between the coroplast and the wood. I haven't had any chewing yet although always keep an eye if you put up a first floor because they can stand on things and reach it. I Also used wire like the one in this link (broken link removed)
Also no need to cut the wire creating dangerous pointy spines, all you have to do is bend it flat at a clean edge and keep bending it back and forth a couple times and it will just break naturally leaving you a nice clean edge. Still don't put the wire on the inside, put it on the outside to be even more safe as we don't want any Peggy's cutting they're feet.
Hope this helped!