It wasn't that long ago that a gay character in a novel was for comic relief or acted as a dire warning. Luckily, modern times gives us a far wider range of options.
In our modern times we are quite fortunate to have a range of characters on TV, in movies, and in novels that represent gay, lesbian, transgendered, and other groups. We are finally at a stage where a lesbian character isn't automatically a butch, masculine female in a suit. A gay man doesn't automatically swish when he walks with a limp wrist, decked out in pink flowers. Certainly these are one aspect of these groups - but they are not the sole one. We can now represent the rich wealth of humanity in all its beauty.
So certainly you can start with some of the "stock stereotypes" if you wish, to make a point in your story. Your gay hairdresser character can speak with a lisp, sashay from place to place in his floral clothing, and drool over new shoes. However, it could be quite more powerful to have a person who looks the part enter a room, and then to end up being quite different. Perhaps he opens his mouth and it turns out he's a stockbroker who has a quiet, steady voice and speaks seriously at length about the state of the banking industry.
It's become a cliche that the handsome man or the beautiful woman is "unavailable" because they sleep with the same sex. Even music videos like "Call Me Maybe" play on that, as singer Carly Rae Jepsen tries in vain to draw the attention of her studly neighbor, who turns out to only be interested in her male guitarist. Think outside the box for your characters. Maybe the English schoolteacher who everyone assumes is gay is actually pining for the woman he loved, who died many years ago. Maybe instead it's the Spanish teacher who's dating someone new each week who is doing this as a cover for her decade-long love of another woman.
Think, too, about cultural issues. While it's challenging for all people of all colors to be gay, there can be extra challenges if someone comes from the deep south, or from the Bible Belt. How might they handle sermons in church, or anti-gay humor of their friends?
Come on by the forums to share your proposed characters and dialogue. We'll be happy to offer ideas and suggestions, to make your characters as authentic and rich as possible!