You and me both, brah. The story shouldn't rely so much on the expanded universe. They should be more like Star Wars that also has expanded universe but the movies tell their own independent story. I hate this about Halo. The story has gotten worse and more difficult to comprehend as the games go by. By the time ODST, Reach, Wars and shit started happening I gave up.
I've played only Halo 1, 2, 3, and the beginning of ODST.
From my exposure to cutscenes and terminals (I have never read anything on Wikipedia or read books or watches Halo movies or shows):
-I am guessing that the Didact comes from a race of people called "Prometheans". The Didact may or may not be a "Forerunner". Either way the Didact had some hand in the planning, engineering, and creation of the original Halo array. The Didact is a male with terrible temper, quick to anger. He has a foil companion, a female called The Librarian. Don't know much about her from Halo 1, 2, 3, and ODST, but there was a suggestion that having The Librarian around would be great because she is level-headed and would know how to solve any problem related to the Flood. However, wherever the Librarian goes, the Didact follows - so be careful what you wish for: if you want The Librarian you have to deal with the Didact too.
So I gleaned all this from even before playing Halo 4, without ever touching Wikipedia, a book, a show, or a movie. Sure I may be wrong with some of my guesses but I have a baseline to start with. I find it mystifying that someone can start Halo 4 without ever hearing the word Didact beforehand and thus having no clue/context about him. When people say "I'm very annoyed that you have to know about the expanded Halo universe to understand Halo 4 or Halo 5" please god, don't tell me these people are including the Terminals in this discussion, are they? The Terminals are a wonderful, incredible reward in Halo from my limited experience. They provide so much great backstory and they are available in-game (at least in MCC...). I don't think I would ever begrudge Retro Studios for including deep lore in their scan logs like they did back in the Gamecube era.