I am working on a near-hard scifi story that mainly involves travel across a single widely populated solar system. I imagine that realistically there will probably be a wide variety of ship designs, but fuel types will probably have to become more standardized, much like different levels of octane grades in gasoline for cars, or diesel as an alternative all together. Assuming there's still a higher prevalence of more traditional rocket engines (rather than super booster engines fueled by handwavium) what are the advantages or disadvantages of using liquid hydrogen or liquid methane as the base rocket fuel?
I am looking to have at least a vague understanding of how they compare to each other as almost everything I find is comparing each of them to kerosene, which as far as we know can't be made anywhere that doesn't have liquid dinosaurs. I am also imagining a variety of craft that travel both exclusively in vacuum and trans-atmospheric. I'm trying to create a world(s) that feels real and lived in, so there should be all sorts of different kinds of craft. Rockets, space planes, bright red hotrod, or whatever the craft, I feel like part of what makes any of it realistic though is having a reason as to why it functions the way that it does and why one might be chosen over another.