Mineral oil is a petroleum byproduct. You do NOT want to put that on anyone's skin. Ewww.
I prefer to use nut-free oils for this very reason. You never know when you'll get a client with a nut allergy who fails to mention it. Of course, any therapist using a nut oil should always specifically ask about nut allergies, but still, you never know when one will slip through the cracks. Then you don't want to be scrambling around looking for your other oil, find out you don't have any, etc. It's not convenient, or professional.
Jojoba is a good oil, hypo-allergenic as far as I have ever known, and has a nice glide to it. I like that one because it's fairly close in composition to the skin's own natural oils, and so the skin absorbs it better than other oils.