There are two different kinds...cotton and nylon. I use the cotton strapping for my purses. I was just at RagShop today and bought some bright pink. They have other colors too. Big fabric stores carry different colors.
ANOTHER IDEA: I used two kids belts to make the handles for this purse. They are cotton, and very thick and sturdy.
Mine are tote bags, but you can see the different kinds of strapping.
As far as making the handle with an adjustment....I'm not sure ....haven't done that yet. But....when you can look at a back pack or other purse to get the jest of it. The plastic piece you buy has directions on the back to show how to do it too.