You can texturing it before or after rigging. I usually do it before, but it doesn't really matter. The only difference is after rigging, you have to jump through a few extra hoops if you come to a point where you have to adjust the geometry.

Editing the actual mesh will not effect texture placement for polys, while it will for NURBS. The UVs are what controls texture placement, and they need to be edited to work for polys.