In my experience, Spivak takes a lot of time to go through the basics (limits, functions, graphs of functions, propertoes of numbers...), whereas Apostol goes into integrals almost right away, leaving all the background material in an optional introductory chapter. Even the introductory chapter starts with a taste of integration at the very start.
On the other hand Spivak seems more mathematically inclined, but he does seem to assume you know nothing besides babsic algebra, and it takes it's time getting anywhere.
My idea is: take Apostol if you're in a hurry, Spivak if you want a solid grounding.
I personally find calculus to be little more than applied mathematics, that is: computational in nature, so I am inclined for apostol who just gets you calculating whereas Spivak, as a mathematician, teaches you the subject by going through the background theory, leaving you with a better understanding.
Also proofs are necessary, you should get used to reading and writing them.
Oh, and
>>11877569 this
