I'd recommend one of the following:
BK5
BK7
BK9
Browning Crowell Barker Competition Knife
None of them are over $150, leaving you with extra cash to buy another knife or a decent sharpener/strop/compound...etc.
I have a Crowell Barker, and it chops really well. I use it to keep the trails in the hills near my house passable. The BK's work well, too, and come across as more rugged and brutish (I mean that is a very positive sense), but something about the handle and blade geometry of the Crowell Barker really helps it breeze thru branches as thick as 1-1/2" or more. Convex edge is easy to maintain, too. Another feature that of the knife is the forward lanyard hole. Put hand thru lanyard so that the lanyard rests on the back of you hand. Twist your hand over, and then under the lanyard in a rotating fashion, and the knife will hover just below your palm without tipping or twisting. It doesn't interfere with chopping or using the knife, and it gives more control than a rear-mounted lanyard does. The balance of the knife is great for this. Best prime-rib and pork roast slicer I ever used, too.
The BK7 and BK9, while not the best choppers BK offers, are just plain great knives.
BK20 would be really hot, but might push the envelope on the price depending on where you get one.
Another option. Get a BK2. They chop well and feel like a big knife, but are small enough to be used for more than just hack and slash. I just stripped and reprofiled two. Put a 20 deg. edge on one and a 25 deg. on the other. I plan on trying them in the woods this weekend and see which angle I prefer. Probably my favorite knife. Inexpensive, rugged as hell, and great personality.
My suggestion would be to get both a Browning Crowell Barker, and a Becker BK2 or BK7. Should be doable for $250.
Good luck.