What I don’t know is the process in which these radicals came about.

A lot of these radicals came from hieroglyphs. The characters are usually classified into 6 categories:

1. Pictographs
2. Indicatives
3. Compound ideographs
4. Loangraphs
5. Phonographs
6. Signs

Check out this Wikipedia article for details. https://en.wikipedia.org/wiki/Chinese_character_classification