I would consider setting up fur part of rigging, but I get your question.
I'd say first model everything, then UV map everything, then add fur, the do the rest of the rigging. That way you can test if you can get the fur working on your geometry and do adjustments to the geometry if neccesary, without risking wasting time rigging something that won't work with fur. Having the fur ready will make it easier to rig the model properly as well, as you will be able to see how the deformations work with fur.