I can't comment on mudbox as I use 3dcoat 3d-coat.com if you mod the mesh as opposed to just stretching/distorting existing verticies then you will have to retexture/uvmap/paint it. 

You could do the whole figure from scratch or start with a base and mod from there.  Of course then you would need to rig it if you wanted to do more then the pose created in the sculpting/modeling software. 

I know some will do some basic box modeling then pull it into a sculpting app, where some will do the whole thing.  Typically then you retopo it in there depending on where you want to send it to and do with it. Retopo is for creating back to a mesh object from the sculpt itself.

I would have to look but there is a nice full workflow creation of a lizard from scratch on the 3dcoat page, its called fullpipeline and the applink demos there for integration with a lot of other apps.