My favorite is the „Dark“ approach. If you go back in time and try to change anything, that is already accounted for in the present. Meaning everything in the present is only the way it is precisely because you time travelled. When you go back in time and try to prevent something from happening, then that is most likely the reason for it happening in the first place.
Let’s say you suddenly had the ability to time travel and said: „Alright, I want to prevent 9/11 from happening“. Well turns out 9/11 only happened because you time traveled, tried to prevent it and inadvertently caused it to happen.
Or: „But what happens when you go back, kill your grandpa, have sex with your grandma and get her pregnant?“ Well, that always was the case. You always were your own grandpa. Because you were always going to go back in time.
It’s quite depressing because it means there is actually no free will, everything in life is predetermined to happen and you can not change anything. Still fun though.