Start with How to Think Like a Mathematician for the move from school technique to proof, then use Proofs from THE BOOK to see concise arguments with structure and style. The Princeton Companion to Mathematics is broader and better for browsing connections between fields, while A Mathematician's Apology is useful for thinking about why pure mathematics attracts some students.
For video, Oxford Mathematics gives lectures and public talks from the Mathematical Institute, while 3Blue1Brown is particularly strong on geometric intuition in calculus and linear algebra. Numberphile and Mathologer are better for short excursions into number theory, combinatorics and proof-led recreational mathematics.
For audio, The Secrets of Mathematics is Oxford-produced and The Joy of Why introduces research ideas through accessible conversations; both are most useful when you can explain one idea back in your own words.
For structured practice, Single Variable Calculus can strengthen calculus foundations, and Advanced Mathematical Problem Solving Resources is directly useful for advanced problem solving. Oxford Mathematics 1st Year Student Lectures gives a taste of first-year Oxford pacing, while AP/College Calculus BC can help US applicants check the Calculus BC fluency expected where that route is available.
A balanced plan uses one resource for proof, one for problem solving and one for broader mathematical culture. Reflection matters more than volume, so keep notes on definitions, examples and where your reasoning changed.