For someone with high-school level understanding of classical Newtonian mechanics, what would be the best way forward to learn Continuum Mechanics and things like MPM, etc.? Any book/course recommendations?
To actually learn continuum mechanics you need first a good understanding of vector calculus. But this is not necessary at all for using and tweaking particle based methods.
I would suggest to start with the paper I link to below. First skim read it to understand the structure. Then try to follow in detail the parts that interest you most, and play with the code they provide. If you encounter concepts you don't understand, which are necessary for progressing, go look those up on Wikipedia or Google Books (for textbooks).
https://www.researchgate.net/publication/336796234_Material_...
And don't be discouraged by the math notation. It's mostly just shorthand for things you probably understand very well in code.
For example the capital sigma (sideways M) with a letter "p" or something underneath simply means "loop over the range of the index p, and sum up the following expression for the different values of the index".
The capital delta (triangle pointing up) means "difference", for example delta-t is the increment from one time step to the next.
The upside-down delta is the Nabla, which means gradient, which means derivative in each spatial dimension.