I've been looking into reading the other books from the Lord of the Rings universe that Tolkien wrote. Where should I start?
The Lord of the Rings is fantastic. It is an by an Engish novel by JRR Tolkein.
Can you tell me what I should read if I want to learn more about the history of that written universe? I think the name of it starts with an s.
Seeing that I have only read The Lord of the Rings I am only knowledgeable on this very subject. I do know it was a sequel to "The Hobbit".
I wonder how The Hobbit was made into three separate full length films even though it was just one book.
You could ask someone that is knowledgeable about "The Hobbit". Since you are so curious about The Lord of the Rings, it has sold over 150 million copies. 
Where does that put it on the list of best-selling book series of all time?
Around third. The Lord of the Rings villian is the Dark Lord Sauron. He created the One Ring that rules the other Rings of Power.
How many other Rings of Power are there? And who were they given to?
I would not want to spoil too much for you since you are so curious to read The Lord of the Rings. I can say that the story ranges across Middle-earth. It follows the War of the Ring. The hobbits are the main characters.