>>633147bahco saw I think goes without saying
the gransfors hatchet is a solid choice. I personally went for the roselli 850 forest axe which just suits me better.
I don't know of any knives that have a decent price/quality combo. I have a mora light my fire but I know that isn't THE knife. I had considered a puukko but my view is the thin tang just isn't up to the task.
my ideal knife is about 100-150$. relatively soft but sturdy body with a very hard edge. wood handle full tang with 2 dowel or rivet holes well away from where the handle edges end. maybe there's a hole at the end to run some cord or strip of rawhide through. Leather sheath that keeps the knife secure. blade spine can catch a fire steel. I kind of like the profile of B in the picture for that purpose. then the blade edge is just a straight bevel.