I'll use art sinew, dacron (hey, it's useful for something
) waxed lined, heavy outdoor thread, saddle thread... pretty much anything to stitch a grip. Can get some of it at pretty much any craft store.
I buy a lot of leather and have a bunch of offcuts that are perfect for grips. I'd advise
against buying leather from moscow hide and fur. I use them when I'm in a pinch, but have yet to be satisfied with anything other than fur from them.
The swatch books from furniture stores is a great tip to get small pieces of the thin leather that's perfect for grips!