Rather than first approaching this from "what are my keywords and how many can I rank for?", I recommend you first figure out content and sections that should appear on your homepage: Communicate what your site is about and help your visitors to navigate your content/products/whatever it is. Once you have the different sections, content and keywords will fall in place.
However, as KingZen said, it is easier to optimize on pages that are topic- and keyword-dedicated rather than on your homepage. You also do not want to "confuse" google etc. whether a dedicated page or your homepage is the best result for a user's query.