I am looking for something that can secure me when I am on the edge of a cliff, so if l fall it wo not break? What kind of slings, or webbing is usually the best (strongest) for this?

Slings r basically webbing sewn in different size loops & r used to connect the pro or gear placed in cracks or on bolts to the lead rope & r made out of slightly smaller & stronger webbing for lightness & practicality. Webbing on the other hand is sold usually by the foot & comes in some different widths & is often used for belay anchors, rappel anchors, & top rope anchors. This is what u would be better then slings for keeping u anchored to the cliff edge. You could also use 6 mm cordage that is designed also for belay anchors. Maxim makes a 25 foot spool that is reasonably priced.

If u do not mind, l went back & looked at some of ur questions. l was not sure what u were going to be doing with the answer u get. It concerned me in that l hope ur not trying to learn climbing technical skill & knowledge on alone & that u have the acquittance of people that r knowledgeable. It is a very dangerous sport to be learning by trial & error. Your questions have had some knowledge but not a lot, & l worry l can not help it, for ur safety & for the validity in the public & governments eyes for the continue freedom of the sport.