The other day I told you about some of the things you'll need to be concerned about but where would you really begin? It would be the sewing part. With your first bear you'll want a fabric that's easy to sew, easy to obtain and doesn't twist. There are lots of decent fur fabrics you can get locally but to learn on I'd recommend a plush felt. It's basically felt with fuzz on the top. It comes in white's, tans, browns and black. Once you work with it you'll want to keep using it!
The bears on the right are made with plush felt.
If you were making an heirloom bear you would order wool felt for the paws but I just buy felt locally. I do wade through the stock though. Some sheets are thicker than others and the thicker the better.
A quick note about other furs. You'll want to try them and you should but wait. Every fabric does something different. One I used stretched out and another twisted when sewed. Sometimes you can work with these problems and sometimes you can't. Try the plush felt first because it won't give you any problems! I want to encourage you not discourage.