Like everyone else I will tell ya Good Stuff to Go for the ribbon needed. More important, GSTG sells the various 1:6th scale buckles you need to really make your sling truly functional.
Now that I said that, lets take one more step in the right direction. When it comes to making slings you will start to go through a lot of ribbon after 2 or 3 weapons. GSTG sells their ribbon in 72 inch length in various widths. Additionally, once you start making slings you will come up with other applications for the ribbon. It is just natural.
The type of ribbon you are actually buying at GSTG is called Grossgrain ribbon and can be purchased at Michael's or a variety of fabric stores in a variety of colors, lengths, and widths. You are going to pay good price for those 72 inches at GSTG. So, why not get 10 yards for $1.50 at your local fabric store or eStore?
While you are at your local fabric store buying Grossgrain ribbon, get you a mini-iron. It is a hand held device that has a very small flat pyramid shape tip to help dress makers, tailors, etc. iron a helm, etc. in very small places. The mini-iron also has a switch to control the amount of heat coming out of the tip. What this device means to you is: for those application where you want the ribbon stiff and to keep the fibers bonded, heating it with the mini-iron will accomplish this.
BTW, here is a sling diagram to help you along.