My pick would have to be the A Whole Nother Story trilogy, in which (spoiler warning) you can only travel back in time. But because time is in a loop of sorts, if you go before the beginning of time, you will be at the end of time. From there you can go back to any time you want to. And time paradoxes cannot be produced. Plus, your memories from the previous timeline exist as well as the memories from the new one.
The End of Eternity, by Isaac Asimov, 1955
There is a place called Eternity, a place outside time that watches over every possible ramification of time based on every single different choice a person can make and those who work there can travel time by a lift, and they do it to fix things that can put a timelime at risk