Confession: I have a story that has been unfinished since 2013. I will finish it. I have been writing subsequent chapters in my head for two years. There may not be anyone left to read it, but I'm determined to finish it.
Re AU stories: The best ones are those that can stand alone without any knowledge of canon, but having the canon as background makes it better. Three examples of "House" AU fanfics that I love:
House is a centurion in ancient Rome named Gregorius, and his BFF, James Wilson, is his slave, Jacobus. Despite being master and slave, they are friends.
Civll War setting. House had been a troublesome Army surgeon and was now a transport agent (person who transports the bodies of dead soldiers home for burial). Wilson is the soldier whose body he is transporting -- he and Wilson's ghost converse during the journey.
House is a tree stump, and Wilson is a butterfly. No, really!
House and Wilson's relationship -- what some have called a "bromance" and what Wilson himself once called "this stupid, screwed-up friendship" is at the core of the series. Knowing about all its bittersweet dynamics in canon makes reading the AU stories a richer experience. But any one of those stories, especially "The Stump and the Butterfly," is a beautiful piece of work on its own.
By the same token, watching "House" is probably a richer experience for someone who is a Sherlock Holmes fan than for one who isn't. The show made no secret of the fact that was inspired by Sherlock Holmes, from the names of the two main characters (House = Holmes, Wilson = Watson) to the random references throughout (House's address is 221B, the gunman who shot him in Season 2 was named Moriarty).