In the last few chapters of the story I'm writing, the main character is forced to go into the future and see how "things go wrong". He goes back to the present and fixes what needed fixing. Because of the nature of the story, the plan is for the timeline to be overwritten. So, when someone goes into the future, not the past, goes back, and changes events, what paradoxes should I worry about, and what happens to the traveler, being in the timeline that being overwritten while it's going on?
Well there are varying theories, but in my mind, if you go to the future that is how it will be, as that is the future. Even if one were to then go back and alter the present, that would have already been taken into account in the future, and your first visit will have the same alterations of the second. For example, if I went to the future and saw that my best friend was dead, then went back to the past, in my opinion it wouldn't be possible to stop their death.
It's called "the grandfather effect." That name is based on the paradox of going back in time to murder your grandfather. If so, would you exist to go back in time to murder your grandfather... Are you writing new screenplays for "Quantum Leap"?
If you subscribe to the infinite universes (or multiverse) theory of time travel, I don't think you have anything to worry about. Your guy sees the future, goes back and alters the path of time, creating a new future. No paradoxes to worry about - it's exactly the same as if he'd seen the future in a crystal ball. However, if your story had used fixed time theory - the idea that everything that happens is inevitable and cannot be changed - then you would have had issues. Change things to prevent someone whose destiny is to die, and the universe would just find some other way to kill them (cf. Final Destination).
I started a time travel thread a while back and received some great starting points for research. I think it could be helpful. https://www.writingforums.org/showthread.php?t=39779&highlight=
What happens when you character goes forward in time and runs into his future self? Makes me think of Back to the Future. Then I wonder what I would do if a past version of myself showed up told me "Things are messed up now but I can fix everything Trust me." How do I know he won't mess it up worse? I might be tempted to stop him.
See Primer - very original and deals exactly with your issues. NOTE: Quite a few Sci Fi Publications specifically list your plot as one they do not want to see. Just a note.
Excuse me, but a writer who asks a question like this should come up with his or her own answer and make a story out of it. Work out the consequences yourself, and explore the logic for internal consistency. Create your assumptions, and try to tear them apart. This is how stories are built. Not by asking others to do the thinking for you. This isn't research. There is no factual answer to your question, given that there is no single accepted theory of time travel supported by experimental evidence.
As an older guy, I would tinker a future where I benefit, then go back in time and sell the time-machine to myself as a boy, supporting my new lifestyle. He can drop me off in Paradise while he builds his own future.
A good way of dealing with this would be the predestination paradox where your character ends up accidentally causing the future he is trying to prevent. The reasoning behind this, is that whatever happened, happened and that events in the future already accounts for the time traveling.