Assuming you have a strong high school background in math and good ability, and given that CS is a strong possibility, I'd suggest going through "Mathematical Thinking: Problem-Solving and Proofs" by D'Angelo and West. It's an overall introduction basically to what's in the title, and it covers various areas including some discrete topics.

If that book proves too difficult, try reading "Journey into Mathematics" by Rotman instead. It's shorter and easier.

If you choose multivariable calculus in the end, I'd suggest "Advanced Calculus of Several Variables" by C.H. Edwards, and if you find you don't have the background for that, then "Multivariable Mathematics" by Shifrin.