Started a Homebrew (first DM ever) and I could REALLY use some help!

So, I started my own idea for a campaign, and I the players seemed to really like the idea.  We're a time/dimension traveling agency hopping back and forth to save important heroes because cataclysm is imminent and reality is coming apart with adventurers and heroes having become so scarce.  The idea is, we're a group trying to find the right way to intervene in situations where there was a total party wipe and stop that from happening so they can continue in their adventures. 

I have some imagination, but not as much as I'd like.  Do you guys have any suggestions or past experiences on fun, crazy, or harsh experiences in campaigns where things took a bad turn?  And if possible if you could include some vague details on what classes, levels, enemies we're involved and the setting it would be greatly appreciated... and the motive for the party to have been there.  Thanks.

Have the players actions in the past come back to screw them over in the future.  For example, save someone that starts an organization that starts out good and eventually turn to evil.

And/or do the reverse - have a friend they meet later originally be an enemy and their actions turned him friendly.

Have a blatant paradox that is unexplained.  Wait a second, how can we kill George when we know he is alive later?????

Have some people be really mad at the party in the future, but they do not know why until they go back in time and screw over that guy.

I was in a similar adventure once, where a dragon broke loose in a time-traveling organization we were part of and killed everyone except for the modrone operator of the time machine. We then traveled to some other planes and eventually Eberron, where we were at first trying to kill some Yuan-ti and take their cargo until the former, now dead leader of the organization popped up and tried to take the cargo - the egg of the dragon that massacred the headquarters of our organization. It was a pretty good twist. 

I would recommend doing something like that. Make people not as they seem, and have the characters fight the past or future version of those people. They then go back to the present and confront the person. Drop backstory of things that have already happened in the timeline into the past, and the impact of things currently happening in the future. Play into the funky nature of the time/dimension-jumping nature.

In a movie, the writer has complete control over the characters and complete control over what the audience sees. Time travel movies can work because the writer can set up the story, throw the characters back in time, remove certain things so an easy fix isnt possible, and then have the plot focus on something relatable, like mom and dad need to kiss at the under the sea dance. And it can all.be done with out creating paradoxes because the writer controls the characters. Or a paradox becomes the central plot hook the charavters need to fix.

In a campaign, time travel can be extremely complicated because you are a dm, not an author. You cant control what the players do.

Ive  had a time traveling npc as a long running charavter in a campaign. The players did some extremely limited time travel stuff. And i was able to prevent paradoxes. The goal for me was to make sure at the end of the campaign, everything made sense.

If youre doing a "time travel all the time" campaign, it sounds like you might want to consider watching Quantum Leap for a way to put the players in different times, and give then the goal of preventing a tragedy.

The alternative is just do an infinite worlds multiverse where paradoxes dont create problems, they just create another verse.  See also Dr Who, who handwaves paradoxes away with his "Wibbly wobbly timey wimey" catchphrase.

The halfway point between "back to the future" style and "wibbly wobbly" style might be the "Loki" series.  Which has a multivers backdrop, but also ran into a paradox of sorts at the end. Really good series.