Get a nice multi tool, one with a vicegrips.this is for repairs to gear, pulling splinters. Tape a scalpel blade to it. This your tool for working on your bod. Tape half a hacksaw blade to it. This is for cutting metal. (these are used by holding in the vicegrips. ) Get a wire saw to cut wood. weighs nothing. Get a solid 4-6" knife, with a good non slip handle -this is to cook, cut misc. items, etc. A river rock will sharpen just fine , find a smooth hard stone. And if you want an hatchet --get a hudson bay axe. Lightweight and will do a hundred times the work of a hachet. A hachet is primarily a tool to split kindling. And an E-tool comes in handy also.
I don't know if the Snow and Nealy axe company, Bangor Maine is still in biz., the woodsmen in my family swore by them.