What follows is about careers (as asked) rather than specifically about University entrance.
Yes, the more maths the better for just about any career in science.
Statistics is particularly helpful. In addition to what you get in most curricula I’d add the importance of statistics in everyday life and in politics. Listen to More or Less on Radio 4 and browse FullFact.org. Those will give you lots on how to think numerately, which is rather different from cookbook statistical exercises.
I’d also encourage you to do mathematical puzzles. Anything by Martin Gardner or Alex Bellos, who runs a series in The Guardian. If you attempt them working in groups they’ll also help with collaboration.
I am a statistician – the more mathematical skills you can gain the better. I work in applied areas – estimating parameters from datasets (on Ebola in West Africa, for example). Mathematical skills underpin understanding statistical methods and computer coding helps turn that understanding into results.