This is an enormous amount of material, mostly aimed at beginners, including several books. For an introductory overview, let’s highlight one paper, Physics, Topology, Logic and Computation: a Rosetta Stone; if this paper doesn’t motivate the reader, then they shouldn’t force themselves to chew through hundreds of pages of textbook material.
While a textbook can be a decent reference for learning, I have found that nLab articles are usually more well-rounded, including many different perspectives on the usage of various structures and universal properties.
Nice. I got “An Invitation to Applied Category Theory: Seven Sketches in Compositionality” for Christmas. Pretty stoked to go through it. I’m only through the intro and the beginning of the first chapter, but it is pretty well written.
This linked to: https://github.com/prathyvsh/morphisms-of-computational-structures which I found very useful, there was a cool interview with Robin Milner and many cool papers.