I'm also using the cement mixing tubs with 1/4 mesh on top. They are probably a bit bigger than necessary but I've had no chewing problems.

My construction is furring strips (called 1X2 but really about 3/4 of that) held together with 1.5" drywall screws. With proper pilot holes you can build some neat but cheap and light things with furring strips and drywall screws.