Stuffing sticks are available, although the handle of a wooden spoon or chopstick is equal to the task. This thing finely shredded wood looks like straw. These days, woodwool is available from specialist suppliers. An important use is for stuffing the nose which makes embroidering much easier.
Polyester is the most common filling available and is extremely easy to use.
There are many different grades and qualities. Kapok is a material that is very silky to touch, but as it is handled, the fine fibers float around, so wear a dust mask. Kapok is best used for small and miniature bears since it gives a 'weighty' feel as it is packed in. Pellets are available in plain and scented varieties. Glass beads are easy to use.