I would say a nice 5/16" braided nylon rope would be the most utilitarian. Polypropeline stretches too much and hemp is not as strong. Just make sure to whip the ends of the rope to prevent unraveling.

Twisted rope is fun to learn how to splice with but not very strong either.

For safety/rescue work I wouldn't use anything less than 1/2" braided nylon and in mint condition. Safety requirements would be too high for anything less.