Does anyone know what style/category this type of illustration falls under, and any tips on where to learn more about this would be appreciated.
That looks like mid-century modern style or mid-mod for short. It is characterized by quirky angular characters, cartoon eyes, and bold vintage colors. Some Hanna-Barbera material is similar such as the Pink Panther and the Flintstones, so you might also find examples by looking for the Hanna-Barbera style.
In your example, there is also a limited palette and very obvious halftoning.
Searching for "mid-century modern illustration" on Google, you'll find much more: examples, tutorials, brush sets, palettes. YouTube also seems to have some resources.
It is trending again in 2019 as modern mid-century modern style. Here is an interesting read about this which also includes a bunch of nice examples : https://99designs.ca/blog/design-history-movements/mid-century-modern-design/