Well, I have never had one but I am sure a derringer would beat a stick, can of mace, rock, etc. I saw a video of a guy shooting a .45-70 derringer and was surprised that it did not recoil as bad as I thought it would.
I can't decide if I were to get one what caliber it would be but, being that it would probably be used in a life and death situation, I would probably want one that would be the biggest caliber I could shoot, at least once. Also, I believe I would want a double barrel model, for 2 shot availability.