Some one mentioned Cheness, only make katanas, but They are one wicked cutter. Bought the SGC series, which was made for cutting tatami/ goza.
http://www.chenessinc.com/sgc.htm Got the "tsukikgage" Katana. I paid $300 for mine (they are $400 now). And These will go through ( with a correct cut ) a 4" tree. I HAVE done this. Not "saw on youtube"
And even when my form wasn't so great, the sword dug in, twisted in the tree, took some work to get out. And the edge wasn't even rolled. Never seen anything twist in a tree and not have anything happen.
The SGC series may not be what you are looking for, at 3lbs they are a little heavy. Not really quick single handed. The SGC ko-katana would be an awesome size for general cutting needs.
Easily cuts water bottles, bamboo, any type of mat, and if you want to test it. Pretty big trees.
On a "cheaper" note
If you want something, user friendly, and "battle ready" you can also buy a cold steel machete. Have a 24" and the kukri machete. Stamped high carbon steel, requires some sharpening. But... In a situation I needed a blade. What I would grab first. Paid $16 for the kukri, $9 for the machete. Just ordered some shorter ones for about $9 a piece. I Would trust one of these more with my life than most " battle ready" swords. Because they work, and never break.
The kukri took apart a few pallets, nails and all. Had a few nicks in the blade where it hit the nails. little bit of grinder, good as new, and near shaving sharp.
If you want something indestructible, Buy a machete. You could buy a truckload for $500. Or a good kukri "never broken in battle" is always a good thing to have said about a battle weapon.
If you want a functional sword, buy cold steel or cheness.
Paul chen (hanwei) sword are a good sword, if you know how to use it. But they Are not as tough as others.