Thanks for sharing your question here on CareerVillage. I hope you find helpful information and answers from the caring volunteers who use this site to answer student questions. It’s great you are sharing about your career interests in music.
Here are some resources you may find helpful:
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Melisa recommends the following next steps:
Those three things you listed can sometimes be entirely different careers for three types of people or occasionally there are people like Zedd who end up covering a lot of those bases even while working with other people. So there's no direct path to being any of those three things. However, a common thread among people who do these types of things is hard work and getting experience wherever you can. I know that's vague but there aren't exact requirements for any of these jobs. What you can do is find projects that interest you and work very hard to make them as good as you can. Even cheap gear can work to record songs you or friends have written. Finding people or projects that interest you will give you the opportunity to work hard and that will lead to more opportunity down the road. Use what you have to get better. It's how everyone gets started.
If you have more specific questions about training, gear or how to find projects, feel free to ask!
Kyle made an excellent point when he mentioned that the three things you listed can be very different careers. If you're just starting out, or consider yourself more of an independent learner, I would also suggest working with a software program called FL Studio 20. It gives you the opportunity to compose, work with different instruments/vocals, and arrange your projects. For formal training, check for audio engineering programs in your area (Recording Connection is one of the better known organizations, but local colleges and Art Institutes may also offer degrees in this field). I hope this information helps, and best of luck with your career!