For a budget of $100, I would start with a CRKT Stiff Kiss MDP, available with a partially serrated edge if you must, for about $20 from internet sources.  Light and strong for any reasonable use, a really great backpacking knife.  The rest of your budget is available for a multitool.  I really like the Wave, but it is unnecessarily heavy, and overkill on tools, for backpacking.  Absolutely superb for situations where you are not counting ounces.  I am extremely retro in that I still carry the original PST for backpacking; it is all I need and reasonably light.