If you're new to programming, it might also help you to get started with Max/MSP and YouTube videos that already show you how to make the mini-synth you're after (terrible as a programming environment but great as a learning/prototyping tool).
The Computer Music Tutorial by Curtis Roads is a good companion here if you want inner workings. You might be able to snag a PDF copy online to see if it's for you.
Audio Programming Book is entirely in C and can be a bit of a pain to get things working in C if you're new to programming (although highly worth the initial struggle if you're looking at it with a career in mind), although I'd still recommend stepping from Max/MSP into MATLAB/Python, which focuses on functionality rather than programming itself.
Python is also bit more beginner friendly, although C++ will probably end up being your long term bet.
I'd pick up the Pyo library for python, and/or a tutorial like this one, after dabbling with Max/MSP a bit: https://python.plainenglish.io/build-your-own-python-synthes...
Then if you want to get even deeper into the DSP, you could go with pretty much any of the other resources the others have mentioned here. My personal faves are the Steven Smith DSP book, Julius Smith's resources (with its runnable MATLAB scripts), and DAFX book by Udo Zolzer.