Help!

I have smooth binded my character and there are many deformations that I do not like. Currently the shoulder and the elbow so far have been causing me problems. I do not know which direction to go to. I have been currently looking at rigid bind and it seems promising. Should I go this route? My character is like a body builder so I want to keep the huge muscles, but allow the joints to deform the skin realistically.

Also, please take a look at the wrist. The wrist deforms very strangely or correctly, but not the way I want it. I have seen some modelers rotate the geometry prior to skinning to correct this. Should I go in this direction?

Any advice would be greatly appreciated!

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The problems you are encountering are three of the most common hurdles in the quest to get realistic deformations on a skinned character.
There have been countless methods developed to get better deformations in all of these areas.
Many people get their start/make a living by mastering realistic deformations.
Extra joints, corrective blendshapes, influence objects, MUSCLES!
(Changing geo as you mentioned too!)
This is just the tip of the iceberg.

To answer your question, I think your time would be better spent learning any or all of these methods before you spend any time learning Rigid binding.
While Rigid Binding is a powerful tool when used correctly, it will still only get you so far.
You will still need to spend a chunk of time adding advanced deformations.
Especially for a big muscular character.

I know Maya help has a good break down of influence objects...for a start.
A couple of advanced arm/leg rigging tutorials will give you some different methods as well.
Look around and I am sure you will find a method that you can sink your teeth into.
All the best.
~Ben