I'm a Junior in college majoring in accounting, I may be able to help. You need to look up the requirements for sitting for the CPA exam in your state. In a lot of states it is required to take part in a Masters of Accounting program (MACC) to be eligible to sit for the CPA. A big part of attaining an accounting job in the big 4 accounting firms (public accounting) is the recruiting at your school so find which college in your area has the best hiring ops by public companies.
To answer your questions directly:
Courses are worth taking in college:
This isn't really an area where you get to choose. Your undergrad will be mainly laid out for you, typically you will take
1) Intro to accounting
2) managerial Accounting
3) intermediate accounting 1-2 or 3. (This is a weed out class at most universities)
4) Cost accounting
5) Federal Taxation
6) Auditing
ect.. you get the picture. There are classes that every school must make their students take to be accredited.
Where you can change classes would be in your pursuit of a minor. Accounting majors typically aren't good at writing reports or communication which is a huge part of the job you will be doing after you have your degree. English, Philosophy, communications, or a technical (STEM) minor is always a positive.
What colleges are worth looking into
Answered above more or less, check into which college get recruited heavily by the Big 4 (this is: PWC, KPMG, E&Y, Deloitte& Touche)
What I can do in my senior year of High School to help me reach my goals.
Honestly enjoy it, you're not going to get ahead of your college classmates much by studying more in high school. That being said, try to get a good grip on journal entries and how each account ties to one another.
Accounting internships require fairly competitive GPA's in college and you should shoot for a 3.5 ideally. Also look into joining Beta Alpha Psi if it's available at your college (accounting fraternity that deals with getting internships more or less)
Additionally:
MBA's aren't super common if you have your CPA and MACC already done. That's something you would shoot for if it were required to move up in a company.
There are a few different fields within public accounting: Taxation, Audit, Assurance ect.. Know what each one does. I was surprised to find I liked taxation more than I thought I would. I'll be trying to find an internship in Fraud this summer though.
Expect to work 80+ hours a week with a public accounting firm and be traveling (at least in audit) for at least 80% of the time you are at work.
Try to figure out what you inevitably want to do with your degree, if it's being a CFO or controller the CPA is a great way to get there. Also a lot of people find they actually enjoy finance more than accounting by the first few years (CFA professional degree).
To give you some perspective I'll be double majoring in accounting and computer science so that I can develop accounting systems and high frequency trading systems after I graduate. There's a lot of possibilities with an accounting degree.
