So far I've tried:
What I've found is that fleece and flannel sew the best. Fleece is a bit thick and strechy.
Flannel is just as soft but before you wash it you should use pinking shears on the edges. It frays really badly otherwise.
Flannel stuffs well and streches a bit when stuffed. It's soft to the touch and can be stuffed floppy and firmly.
Fleece stuffs nicely as well.
Felt is rough and stuffs very stiff. It's not much fun for me to use. It's pretty cheap though.
Faux fur is a pain in the neck! It sheds while you're cutting, sewing and stuffing. It's hard to turn right side out and a bit of a pain to sew becasue it's so thick. It barely streches and stuffs very firmly.
Cotton should also be pinked around the edge before washing. It's a nice fabric, not soft but not stiff. And it stuffs very nicely. It can strech a bit depending on the bias. It's easy to work with and is not to expensive. Works pretty well for hand sewing too.
Knits are a bit tricky for a beginner. It streches a lot! and it's a bit hard to hand sew. It can be expensive and the fabric has a tendancy to roll on the raw edges. It does stuff well though since it streches so much.
My recomendation is flannel or cotton. Becasue they both work nicely with beans or plastic pellets inside.
Oh and Always remember to wash your fabric before cutting and sewing. It can gum up your sewing machine and change the look of the fabric. and some fabrics shrink in the wash so it would be horrible if someone's little buddy shrunk after playing with it.