An axe, I'd go a Council Sport Utility Hudson Bay,you can get them with 18" and 28" handles, or maybe a Husqvarna carpenter's axe.
I'm not a fan of short handled axes, but they do have the uses at times. That said, with what you want, I'd be looking at a Tomahawk.
Get a Cold Steel Frontier. They are a little rough to start with but CHEAP. Get a few handles, sharpen, removedthe set screw and reseat the head. Tomahawks are impressively useful. I've cut the [bleep] out saplings around the place up to 6" trees. You can also remove the head and just use it as a 'knife', skinning tool etc etc.
I've put together so damned many axes in the last year and have a basket full of heads and handles waiting. I'll snap you a few pics tomorrow to show you a few.
Like I said, don't underestimate the usefulness of a Hawk and if you are really out there and bust a handle, it's no trick to make a new one from a stick. No wedges needed.
I've also put some riggers/carpenter heads on longer handles that are quite useful. I also like putting hatchet sized heads (1 1/4 pound) on 24" handles. The swing past their weight class.
Aside from the Tomahawks, which have 22" handles, I generally don't use anything less than 24". The shorter they get, the more dangerous they become and less useful.
Guess I'm looking for a hatchet more than an axe. Post some pics if you could, I'd appreciate it.