Well, as far as I know, there are only two types of time travel that are self-consistent: alternate timelines, and closed timeloops. I find the former unsatisfying, because you aren't really travelling to your past (and because, functionally, it leads to your disappearance from the original timeline), and most stories with the latter are poorly executed. If anybody knows of anything else, I am all ears!
...I once tried to write down the rules for some sort of quantum superposition of timelines that would allow an approximation of Back-to-the-Future-style time travel that was still self-consistent, but never quite managed to finish.
Yes I am a nerd.