How do I determine the factors to use for the horizontal and vertical axes (e.g., Industry Attractiveness and Business Strength)?

There is no single answer to this question.

The answer depends on the purpose of the analysis for the organization in question.

A way to approach the question is to ask “What is the business case I need to make to support allocating resources to the items (businesses, new product ideas, sales territories, etc)?

See p 176 of Edition 3 of Principles of Marketing Engineering and Analytics for some suggestions.