I am a part of the community, so I can give some of my opinion on what I would personally like to see. Any representation of a non heterosexual relationship would be something that I would want to see in stories. Good relationships, toxic ones, an accurate portrayal of a relationship. Personally, what would be stereotypical is to say that all gay men are flamboyant, or that all lesbians are masculine. Yes, stereotypes are typically based on some form of the truth, but to use a stereotype to describe someone entirely gets repetitive.
Also a common trope in media is that if there are any LGBT couples, it's a tragic relationship and it ends miserably. People really don't want to see just the sad, they want to see the happy. But that doesn't mean make it fake, make it as real as possible. Give an accurate representation on what an LGBT relationship would look like, (which is any normal relationship, but just change the genders around).