Heard many people say that there are three good cal textbooks: the ones by Apostol, Spivak, and Courant. I own Apostol's and Spivak's. The major difference between the two is the degree of rigor and logical order, in which Apostol's apparently beats Spivak's, although Spivak's is far better than most other cal books in these aspects. Want demonstration? Just go to the first section of each book. Check out Spivak's chapter on properties of numbers and Apostol's chapter on real set and the field axioms. Conclusion: Really serious math students and future mathematicians shall pursue Apostol for their elementary calculus education.