What's better: adding new primitives or extrude from existing? This is a very general question. I wanted to know what the advantages and disadvantages of extruding from an existing primitive be over adding a new primitive. To give an example, I have started modeling a hammer. The head is cube primitive. Should I extrude the handle from that cube primitive or should I add a cylinder primitive?

Can a new primitive make it more difficult to put a texture on it? Can a new primitive increase the processing that goes into using the model? Can a new primitive cause problems when rigging?

Please keep in mind that I am asking in general, not only for that hammer example. I am looking for answers that I can apply to all future models I can possibly create. 

Thank you!
I am not an expert, but:

Using only one mesh (extruding from an existing mesh) is absolutely needed if you need deformations, because all geometry is linked, and also can keep vert/poly count lower... it is the better choice in most cases, in my humble opinion.

Using separate mesh (adding a new primitive) could allow to keep independent mesh parts separated, for some reason (e.g.: to split them later while modeling), but also allow you to treat them as a single object in animation (without deformation).