Either one is fine. Most psychology majors require a stats course (or at least mine did and everyone should have one) - if you take AP Stats, you MIGHT be able to skip out on that in college. The course you'd be taking for psych would be a behavioral stats course, though, which goes into research design as well as the relevant statistical analyses, etc.. So, you might not be able to place out of it... I'm not sure what the curriculum for AP Stats is. In any case, if you take AP Stats you'll be way ahead of the game when you need to do your psych stats course. The arithmetic itself should not be difficult for most people, but a lot of people get tripped up on the conceptual part.
More advanced stats is based on calculus (and your AP Stats course might be, too... not sure.) But your undergrad psych stats course would not be. I have taken a masters level research design course which was very similar to my undergrad course (and did not require calculus.) I have NOT, however, taken a doctoral level stats course, but I suspect the sort of course you'd take as a psych PhD would not require calculus, either.
Pre-calculus is not calculus. But, of course you would want it if you plan to continue to calc in college. I CAN say that I took AP Calculus in high school and then both Advanced Integral Calculus and Multivariate Calculus in college... none of which was of any relevance to my psych major, even though my liberal arts college had a very rigorous psych program. Like I said, though, I did not go on to doctoral level work in psych, but I don't imagine any of it would have been needed.