I've always had a
Pulaski, no matter where I've moved. I
became acquainted with it when I was in college -- during the summer I was on firefighting crews, mostly fighting forest fires. We used it both to
clear groundcover, as well as to trench.
It's a very formidable weapon, as well as a great multipurpose tool. If you find one [unlike my link] with a curved axe-handle, it's a very
balanced tool.
Aside from that, I tend to favor short bows for their ease of deployment and quick release in potentially short-range combat situations. I think the
best bows and arrows are those that you can fabricate out of native materials. Maybe now is the time to test out various woods to see which have
the right strength-to-flex ratio. Arrows can be made from many woods, tips cut from sheet metal, and fletching can be done very satisfactorily with
three piece of duct tape, stuck equidistance around the shaft, sticking both to the shaft and to each other, and then trimmed into shape.
Also strongly agree with those suggesting a machette. This is a standard tool where I live, and nearly every household has at least one. There
are, of course, all different grades of them. I like a machette that is full tang. The important thing [to me] is the ability to put a proper edge
on a machette. It's a shallower angle than you would put on a knife, especially if one is clearing bush. Most often done with a file, moving from
the direction of the handle toward the tip. I often sharpen about 5" of the back side of the tip of the blade, for when I want to chop into areas
where I suspect I might cut into rock.