Welcome, John! Hope to see many thoughtful and informative posts from you. (And I like your avatar.)
Yes, you should absolutely, positively read the novel. As you've already discerned, it's got lots more detail than the film(s). Mario Puzo was, above all, a great storyteller, and the novel contains some wonderful stories that didn't get into the film(s)--such as how the Bocchicchio Family provided Michael's safe passage from Sicily; the rise of Al Neri; how the Don arranged for Bonasera to get his revenge, etc., etc.
(Turi and others: Amazon.com ought to give all of us a stipend for the business we've been sending them!)