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I've specifically avoided time travel in most of my stories because it's a pain in the ass to make work.

So, I'd go with the most forgiving version where the act of time travel splits off a new timeline. Or, that the travel itself is to another timeline, depending on how you want to look at it.

That's the easiest to write around, imo. It's also the version most likely to hold up to scrutiny, even if (when) I made mistakes. You can hand wave a lot of stuff when you don't have to worry about paradox.