Database Design for Mere Mortals: https://www.amazon.com/Database-Design-Mere-Mortals-Hands/dp...
This is the book I recommend to everyone who is shy about DB's - I have owned several copies and given every one away. It breaks down not only functionality but how to create a good design in a sensible and easy to understand way. Worth every penny (and now somewhat cheap)
It seems to me that Jim Melton's Understanding the New SQL was pretty good. Anyway, I'm pretty sure I read one of Melton's books when I was learning about databases.
I always thought of the NoSQL movement as encompassing document, KV, and GraphDb's and each can be a major departure from RDBMs thinking. These technologies aren't always "replacements" for RDMB's and often live alongside them, Redis (or memcache) and Solr/Lucene (or elasticsearch) are ones that I have personally used the most.
As you move into other tools like Cassandra or a Graph DB they look shiny but you are making some major (and maybe worthwhile) trade offs. These sorts of decisions probably shouldn't be made based off of knowledge from a book but rather experience and more importantly testing (performance and use).
As a side note, the last project I did ended up using a flat file as a back end because it was fast, simple and easy while meeting the needs for what it had to accomplish. Installing a DB was more work than needed.