As cruelraoul said, there are many excellent contenders which will all do the tasks you outline. It gets to be some pretty fine "slice 'n dice" of properties & characteristics of the knives to pick just one.
I concur with the advocates of a Big 'Un & Little 'Un pair of knives -- a large chopper in the pack and a small light quick slicer in pocket or on the belt. My particular triumvirate for outdoors adds a lightweight folding pruning saw from
Tashiro Hardware in Seattle for sectioning out rounds to split. You could as easily use folding pruning saws from Corona or Silky (or other mfrs) that are more widely available. Here in the NW USA sectioning and splitting are perhaps more needed than elsewhere due to winter wood being soaked from weeks (months) of steady rain.
Next is the Basic 9 .... you don't have a category for belt carry and weight. It wins this hands down.
+1 vote for the Basic 9 as a "do it all" knife. As Peter noted, the long thin (spine to edge) blade is facile & quick in hand, yet has enough mass & length to chop acceptably well. The Res-C adds nice insulation in cold weather and a little traction to grip your hand back in use.
In spite of its lesser ability to fulfill your shelter chopping mandate, my "only get ONE knife" champ is still the Basic 7. It seems to do so much passably well (while not shining at any one thing exceptionally) and carries more readily on the belt than the larger Niner or heavier choppers like various flavor BM's, Killa Zilla, NMSFNO, or SARsquatch. When I head out afield, I want my knife (plus firemaking kit) attached to my body in case things go bad and I lose my pack, so the Seven wins out over its larger siblings through the higher probability of actually having it on my belt when needed.
That said, I did like a lot a
NMSFNO that I tested out before selling it. It chopped well in my uses and was plenty sharp for food. I think it could be pressed into service to perform most knife functions fairly well without being a "no holds barred" champion at any one of them (like the Basic 7). The NMSFNO suffered the nemesis of all 1/4" thick blades in the kitchen -- crunchy veggies like carrots and daikon radishes -- which it tended to break chunks off more than slice off due to their rigidity. Note that I have a bias for Japanese kitchen knives that often are 1/16" or less at the spine -- no kind of choppers, but they slice 'n cut like crazy.
Budget Knives would be either a Swamp Rat Camp Tramp (CT) if you can find one or a ScrapYard Son Of Dogfather (SOD), with the preference going to the CT for its differential heat treat and the utility of the original cordura/kydex sheath with outer pocket for your Firesteel & tinder (fatwood or firestraws).
Money No Object knife: Steel Heart of your choice. My fave was a SH II that I had the matching BM to make the pair.