You are starting an undergrad programme at Bocconi, right? I know many people who went there for undergrad and then went to a top school for masters/PhD in US/UK.
I'm not really sure why you are worrying about masters and PhD textbooks at this point. The math that you need to know is no different from the basic math that any engineering/science/math undergrad student needs when starting university.
It sounds like you are lacking practice and confidence in your math. In my opinion it would be a mistake to tackle something too ambitious in the beginning. (For example there are many excellent, free online courses from MIT Open Courseware in calculus, linear algebra, differential equations, probability/statistics, but they might be too hard for you to start. Or not; by all means, check out these courses for yourself.) From my experience, math is something that is cumulative. When you skip ahead without having firm foundations at each step, it is a recipe for disaster. You'll actually make faster progress in the long run by going a step or two back and going slow.
One suggestion is to start with some high school level books aimed at ambitious students. Take a look at the brilliant set of books by AOPS: https://artofproblemsolving.com/store. They require far deeper understanding than your usual high school calculus books where the emphasis is on routine problem solving. Take a look at the precalculus and calculus books or even the algebra book. Even if it appears too basic, the time you spend making sure you know the basics well is never wasted, particularly for someone like you who has PhD goals. (They also have solutions manuals which make them good for self study.) These books are deeper than Khan Academy courses, which are fairly superficial. After these books, then you'll be ready for the MIT undergrad courses.
This Stanford course called Intro to Mathematical Thinking (https://www.coursera.org/learn/mathematical-thinking), which is aimed at entering undergrads to teach how proofs are done and the basic language of maths, is worth a look. This knowledge will save you hours and hours later if you learn the rules of the game early on.
When you start your undergrad courses (or the MIT OCW courses), you might consider getting and using Mathematica on your computer. It's a great tool for visualizing functions, doing calculus, and a whole lot more. (You can probably get a student license; home edition is also quite reasonably priced.) It's not intended to replace pen and paper skills, but I found that for myself it helped to build intuition when I was learning various concepts. (Also in actual practice and research, i.e. outside your math class, you usually will be using computer tools to do your work. May as well get used to them early.)
For philosophy and motivation, see this first lecture from an undergrad math for econ course. http://ocw.uci.edu/lectures/math_4_lec_01_math_for_economists_introduction_to_the_course.html
(1) AOPS books to get the high school math basics (through calculus) down cold at a conceptual level
(2) MIT OCW - excellent courses that give you a very sold foundations