For a small ax I like a 3/4 single bit ax, a 2 1/4lb 'boy's ax' as it's often called. They usually have a 28in handle and if you find a nice one, I have an older Collins that I like, the head is decently hardened and finished and they chop very well. They seem to run about $15 or so these days. A nice looking smaller one is the Vaughn builder's hatchet, a 28oz model that typically runs a bit shy of $30. The Cold Steel hawks look nice for maybe half again as much.