Dacron B50 is the most common material for making strings, it also comes as fishing line (same stuff)
http://www.thelongbowshop.com/product_im...8_zoom.jpg
Many materials have been used for strings and Sinew was on of the most common for our ancestors.
The English traditionally used Hemp strings.
The Asiatics traditionally used Silk.
For your Longbows (English) you need to learn to make whats called a "Flemish" twist string.
For your recurves you need to make whats called an "endless string"
both can be easily made and learning how to make strings is a must for any self sufficient Archer.
Here's how to make an endless string, the most common type to use. You don't have to spend a lot on "string jigs" as this Archer shows.
http://www.thelongbowshop.com/product_im...8_zoom.jpg
https://www.youtube.com/watch?v=XXdHkYb6...r-Xhmq93Ud
https://www.youtube.com/watch?v=jV9iEY8d...r-Xhmq93Ud
Ps, this guy knows his Onions and is well respected in the Archery community he "walks the walk"