This is a pretty sensitive topic for me, because I studied classical/20th century composition for my undergrad, had to “unlearn” a bunch of stuff that didn’t work for me, and then earned an MFA in electronic music from a very non-traditional program that actually made me a better musician, as opposed to simply being a better “thinker about music.” (Not to talk down about other programs, I am just sharing my experience.)
I would only learn a traditional instrument if it makes sounds you want to make. If you like music with chords, learn about them, their traditional and non-traditional relationships, how tonality works, and what is usually referred to as “common practice.” Get a keyboard, or a guitar, or learn to read/write music and use software. I would also encourage you to look at “species counterpoint” if you want to understand how Bach, Mozart, Beethoven, etc. learned to build music based on vertical harmonies, and how equal temperament tuning influenced tonal music. I’m happy to help answer any questions you might have about these things, and there are probably others on this board who are well-versed in it.
That being said, you could become a great composer without studying common practice theory at all. I completely agree with what Jason said.
If we take a John Cage-ish perspective, music is essentially sound organized with intention. He used chance processes to attempt to remove his human inclinations and habits from the process of composing, and observing the results afterward. This is one approach to composition that is really easy with computers, and is a completely valid way of composing music that has little if nothing to do with common practice theory — aside from the moments when the chance procedures form relationships similar to familiar musical relationships.
Pauline Oliveros made a lot of tonal music, but she also composed a lot of pieces with no notes — scores based entirely on text directions, intuition, and the interactions between performers who compose collectively and in the moment.
Ultimately, I find composition to be about building relationships between sounds. What does this sound do when it’s placed after that sound? Before that other sound? What happens if I play this sound while slowly turning up the reverb? Do I hear that “movement” of sound leading to another place? If so, how do I facilitate that process? What is the relationship between loud and soft? Fast and slow? Etc. etc. Play around, and have confidence in the things you like. If you aren’t sure, record it and listen to it in a week. You’ll have different ears and you’ll learn from it.
That’s how my compositional process works. Play around, find things I like, and see how they relate to each other. And don’t be afraid to share! Hopefully that wasn’t too pedantic/pretentious.