This is odd because genre usually comes naturally with the first few characters but not this time. I have two characters and I know a lot about them except their era/genre. They are brothers, named Tony and Shaun Bradford, somewhere in their twenties, and all I know it's not historical, so either contemporary or in the future - but I don't know the genre. They have been through a lot and their world is definitely not a nice one. All the family they have left is each other. So, any ideas what would fit them?
sure, literally thousands! but if you want to be a writer of fiction, you need to be able to come up with your own ideas and decide which genre you want to write in... no one can do that for you...
Think about what you'd like to write about. What's going to keep your interest. What you'd like to see the characters do.
Do it the old-fashioned way: throw them into a sci-fi setting and watch what happens. Not working? Scratch that off, yank them out, and throw them into current day New York City. Repeat. Repeat. You'll find something, I promise you.
I usually find that I have stories in need of characters rather then characters in need of stories, as that is really what you're saying. The story itself determines the genre. The characters are players in a play, a story, so I find it difficult to start from where you are now. My first short story that I wrote yesterday was about a character I've thought of for the last ten years and I just finally put it down on the computer. The thing is, the character wouldn't exist in my mind if it wasn't for the scene, or story I had to write. Now, I have a blooming series in my mind. In other words, just write your story. Write your characters doing what you picture them doing. If they are not the type that you already have a story for them, file them away for when you need them, and move on to more productive stories that are firing away in your mind.
Throw them together and start a scene where they interact with each other. Just get the story between them and their challenges started. Don't worry initially about the era or genre. Just get them talking and moving. As this happens, they will tell you where they are. Then you can go back and clean up the set dressing. But first just get them talking and doing so they can tell you.
Don't worry about the genre, just tell the story and let it fall into whatever genre it wants. I find that if you've got well created three-dimensional characters then they soon start doing things on their own without your permission. When that happens the story tends to write itself. Just start writing and have fun, if it doesn't work out then start over with them in a new situation and see what happens.
Let your characters decide. Write a bit about their personality, friends, and maybe more about their family. Once you do that, you'll have at least an idea about what house they want to live in or something. Then you can describe your house, and go from there.
I see your point. So many ways and angles to go. I may sound completely insane but why not let your characters tell you where they live and what is going on in there world. Don't force it--I know easier said than done-- but sit down and maybe "listen" to a conversation the two of them have or perhaps interview them. If you know that they have been through a lot than ask them about it how did they loose the rest of their family.
Listen to the people on this page. Only you can figure that out, it's part of being a writer. Figure our what kind of story you want to tell, then tell it! Don't worry about the genre so much. And the setting can be anything that best allows you to tell the story.