I have a good PreCalc book to recommend people. It starts with logic and set theory then moves to the field axioms. It covers a wide variety of topics from there, including the fundamental theorem of Algebra, logs, one-to-one functions and their inverses, trig, imaginary numbers...

http://www.amazon.com/Introductory-A...3&sr=8-3-spell
Though I have yet to read Spivak, I imagine this would be wonderful preparation for it.