Something a bit perversely amusing about a geology student slinging rocks. I wonder if any geologists have come across a stone thrown by some long gone slinger and wondered, "Strange, I wouldn't expect to find this particular stone here, it's quite out of place."

Back to more relevant things. Paracord is very good, especially the milspec. 550 stuff as the quality and consistency is tops. However any quality braided synthetic cord will be fine. Motor mower pullstart cord is very good, strong, abrasion resistant and non stretchy. On the negative, it's a little difficult to tie and is a bit hard on your fingers. There's a very good cord available here that's sold as load tiedown cord. It's white with a single red thread through it, sold in Australia as Zenith brand. As all this material is made in China nowdays I'm sure it will be available in the US too. The only cord to avoid is the common twisted polypropylene type as it is impossible to tie, very hard on the hands and kinks badly.
Anoher possibilty is thin cotton sash cord. Rat Man uses this type of cord on his slings. I have one of his and one other of the same cord. Both very good. Downside of all white cords is that they don't stay white for long.