For artists and collectors sponsored by Intercal...your mohair supplier and Johnna's Mohair Store
I prefer Quilter's cotton as the mohair's backing is usually cotton and using the same fibre for sewing up as the backing is made out of causes less abrasion (if the fibre is stronger than the backing, it could wear it down in time) - using my experience as a handspinner, and years' of working with fibres and making fabrics, there! I found an imported brand (forget the name) which I can't physically break if I try to pull it apart, whereas the polyesters you often can.
If you think about it, those 100 year old bears will have been sewn with cotton or linen thread and they survive just fine. Although technically, the strongest fibre (if processed and spun in a certain way) is pure silk.
I have used Gutterman's which is polyester but only if it's a better colour match when I've done a bright coloured teddy.
For eyes and ears, I buy shoemakers' linen direct from a supplier I use when I make repro medieval shoes for re-enactment.
This beats anything I've found at teddy fairs or in the haberdashers' and is fine for standard teddy colours, and black and white. I've used it for years on handmade shoes and know it can take wear and tear, as the medieval shoes we have made are made inside out then turned, and nothing takes more strain than something you have done that to - then wear on your feet!
I took the advice and used wax on my Gutermann's thread. I didn't like that it was polyester because it was sooooo slick, but the color match was unbeatable. The wax totally did the trick!