A strong base in Precalculus course (US curriculum) is highly recommended. It'd be nice to learn the basics of differential and integral calculus as well, but your university will certainly cover that.
Focus on learning precalc thoroughly, and if you have time, begin study of calculus. However, in college, as Joel commented, retake calculus from the beginning. It takes a bit of "mathematical maturity" to fully appreciate the subtleties of calculus. I've found a lot of students, very clever ones included, just want to bypass their course requirements, and as a result, they end up cramming too much calculus in too short of a time.
As for how to learn, you have some options. The ideal option is to hire a dedicated tutor to compose a curriculum and guide you through a textbook. If this isn't accessible, the internet has great resources. Khan Academy and PatrickJMT come to mind. You can always teach yourself, through a textbook, which would be doable for the Precalc material. However, at a high school level, I do recommend some direct guidance.
You mentioned Khan Academy, and I'll vouch for his videos. They're a great asset, and the bonus is that there's a message forum accompanying every video. KA has a pretty strong user-base, so you'll likely get good community response to your questions.
As a rough guide, you'll want to progress in this order:
As for textbooks, for precalc I recommend:
- Precalculus by Cynthia Young
This is a fantastic, thorough textbook. I use this with my tutoring students.
- For calculus, I like either Stewart's or Thomas'. Both are popular,
so you may want to check with potential universities and just buy
whatever text they plan on using to save some money.
Read the textbooks. Outside of tutoring, outside of watching videos... read! It's challenging, yes, but it's so worth it. If you don't understand something, read it again. If that doesn't work, come here.
Expect to dedicate a minimum of six months for Precalculus study and six months for Calculus I. If time is of essence, don't try to cover everything, but rather work steadily through. Contact a university math adviser to inquire about their program. Remember, a college wants to help you succeed; the adviser will inform of what courses you'll need to take.