No such animal. If you can't pay more than $100 you deserve to die.
The monetary value of one's knife has little to do with whether or not someone deserves to die. No need to spend over $100, no knife is worth much more than that, in the view of usefulness and what you can get for the money.
Can't say it enough, Enzo Trapper, in O1 if you're a purist, S30V if you're in need of stainless. For a traditional bushcraft feel, go for the Scandi Zero grind, it is excellent. The blade is 95mm long (3 7/8"), and the full-tang is thick enough to qualify as a "survival" blade, if you were planning on abusing it. The completed knife will run you anywhere from $100-$150, depending on the steel, but the real draw is the ability to buy blade blanks and source your own handle material and hardware (~$60-$80) or a kit with everything you need included, which you can simply assemble, sand, and finish (~$80-$100). This way, you can rock with your own handle material and fit the knife to your hand exactly, and in the process, make your knife more personal to you.
The Mora's are nice for $15, but I argue that this may be the most high-value "bushcraft" knife out there.
They also have a larger knife, the Camper model, with all of the features of the above, but with a 5" blade, if you prefer larger ones.
Oh, and I would advise against batoning. Get a saw and/or hatchet; your knife will last longer and you will be able to process wood faster and more easily.
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