Fantasy is my #1; I will give almost anything a chance if it has strong fantasy elements. Post apocalyptic, superhero, alternate history, science fantasy, some supernatural, romance, and a few fandoms (especially Game of Thrones) are also likely to catch my eye.
Well, there aren't really any official site rules for it, if that's what you mean. There's no official way which player versus player fighting must be done in a roleplay. There are, however, some things written by Iwaku members here in the Roleplay Institute about how they suggest fighting in roleplays ought to be handled. The Rules of Roleplay Fighting by Sladelius probably has what you're looking for, and it even has a very apt name; he also wrote another guide on the same topic but apparently in simpler terms. Fight Scenes: A Compilation written by Minibit also has some good stuff, including links to a bunch of other good resources for roleplay fighting information.
Hopefully you can find what you're looking for in those threads.