Don't get a knife that is too large to be useful in making other small tools or skinning small game. Quoting: MarPep
You won't be stabbing grizzly bears, but you might be skinning a squirrel. A full tang knife with a 4-5 inch blade is about as large as one needs--it will handle the squirrel, the deer, elk and caribou. It should be small enough to help fashion fish-hooks or scale a panfish.
I have this combo in the santoprene scales. The small cub bear caping knife is pretty much the best knife I've ever used for skinning and deboning meat, does a great job on fish too. [link to ibb.co (secure)
If you don't want to carry an axe you could get away with using the cleaver as a hatchet, I do, and the length of the spine and thickness allows it to be batonned if needed to split kindling. You aren't gonna hurt it. I routinely split mesquite to make chips for the smoker grill, it does the job.
With these two knives and my laplander saw, I can take apart and process anything I come across. Of course the downside is they're a bit over OP's $100 limit.
Smith & Wesson sells a cheap knock off they call the Bullseye camp set for $ 35 bucks giving you the cleaver, caping knife and skinner/gut hook knife. It's 440c so it's not horrible steel, the weakness is the handle, the allen screws that hold the scales aren't allen screws they're rivets and will break if you try to tighten them.
I know because my buddy got that set after he saw my KoA set and wanted it but didn't want to pay for the D2 steel. Let's just say I can skin 8 deer to his 2 before I need to touch up the knives, a quick strop gets them razor sharp again and they stay sharp longer.
Like Mike said, it's totally worth it to get a quality product.