Your best bet for understanding the mechanics and physics of what's going on is going to be to find a good book or two on the topic and giving them a thorough reading. Depending on where you're starting from, what your goals are, what is permissible by rules or budget, etc. - all those types of questions are doing to drive you to what viable options you have and what tradeoffs you're willing to live with.
How to make your car handle by Fred Puhn is a good one to start with for learning the basis in a relatively easy to digest format. The Herb Adams series of books are also good, although more race car focused than street car.
I might be missing something, but typically SAI doesn't change with wheel offset or width. Scrub radius will and that does affect steering feel/behavior.
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