Have a look at this precalculus book (which is available for free from the authors' website):
Remember that in mathematics, it is very important to solve lots of exercises - just having read the relevant section of a textbook is only the beginning of mastering the material! :)
Reading and doing exercises from the book I linked would probably prepare you very well for calculus.
Proof techniques and mathematical thinking:
If you want an introduction to proof-based mathematics (at the introductory college level) a book I liked was Velleman's "How to Prove It".
This free Coursera course is good for that as well:
If you already master the precalculus material and have taken an introduction to proofs as mentioned above (and perhaps read a book on the basics of calculus) then my favorite calculus text is "Calculus" by Spivak. It is very rigorous compared to introductory calculus text, in the sense that every result is proven, and he starts from the axioms of the real number line. If you read Spivak and do a lot of exercises (preferably after doing precalculus, an introduction to calculus and an introduction to proofs) you will be very well set to study mathematics in college. Do not start on Spivak until you have a firm grasp of the material in the precalculus book and Vellemans "How to Prove it". Even after those, it would perhaps be best to start with a gentle introduction to calculus.