This is not an exhaustive listing of all the types of science fiction, but some hopefully focused rambling on what considerations one might have in a science fiction setting. It is focused mostly on thinking about things in terms of tabletop role playing games, but probably applies more broadly to fiction as well.

One possible approach is to look at large setting elements (things like aliens, spacecraft, space travel, cybernetics/transhumanism) and decide how you want to deal with them. This has nothing to do with the rules one is using, at least not directly: if you wish to make a SF-flavoured Dungeons and Dragons, it is extremely doable. So we will talk in generalities about some options for some of the big questions, and how they might be addressed. If one wants a whole book, with worked (instead of illustrative) examples, check out GURPS Space.