Two basic styles are endless and flemish. Each has it's strong points, but get right down to it either one will work just fine when properly made. Targets have been pinwheeled and critters have been killed time and again with both.
There are variations of these, and primitive ways of making strings from natural cordage, sinew, hide, etc. but when it comes to "modern" strings you have endless or flemish. You can make either one from any of the gobs of different materials now available.
Chad