I have yet to see Captain America: Civil War or Spider-Man: Homecoming. Do I need to see both of these, one of them, or neither before watching Thor: Ragnarok?
No. From what I can remember neither Captain America: Civil War or Spider-Man: Homecoming are directly referenced. Thor: Ragnarok takes place around the same time as both of those movies. Besides, the main characters have been away from Earth since Age of Ulron (which took place before both of those movies).
It is helpful to have seen Thor, Thor: The Dark World, and Avengers: Age of Ultron for some background on what happened before this movie started. It is nice (but by no means necessary) to see The Avengers and Doctor Strange as well.