Sometimes I look to what my favorite archetypes are, and try to put a new spin on them. Or simply take ideas from stories you have read or like and make them your own.
I like watching perfectly good characters become corrupted over time, so I have several of those in the planning stages of my story. Or having characters that are hiding secrets from other characters that could be catastrophic when revealed.
When I make my characters, I already know what roles they have and what important events occurred in their lives. I focus on smaller events and explain parts of their personality. Sometimes I make characters based around a motivation or idea and make a background that expands on it, though, I usually use it for groups. Listening to music helps a lot. Occasionally, I get inspiration from a song, anime, or something like that and it just flows out. After I'm done the first time, I go over it again and add or get rid of some things.
It sounds weird, but I let my characters tell me. Inspiration hits, I draw them, and as I draw more of them, I start to learn more about them. I've never really sat down and tried to think of a past for any of my characters; it ends up unraveling as time goes on and I draw them more and think about their person in general.
Work out how you need them to be in the story, and then you can work out how they got like that. E.g. One of my characters was very boring so I figured I would give her a rebellious streak. So then I thought about what in her past and personality would have made her that way.
Backstories can also provide motivation for your characters, so you can think about what your characters need to do in the story, and then think about what in their past would motivate them to do that. Another of my characters has money as a motivation for getting famous. So I gave him a backstory of coming from a poor family who nonetheless supported his dreams, so he wants to be successful so he can support them financially to repay them.
I actually have a random roll chart, that takes a 10 sided die for example
1 - both parents living and togehter
2 - both parents dead
3 - father alive/mother dead
4 - mother alive/father dead
5 - both parent alive, seperated
6 - never knew parents
7 - both parents living and togehter
8 - both parents dead
9 - father alive/mother dead
10- both parent alive, seperated
And a chart for a few years of history, with good things and bad things that can happen. How many brother and sisters they have. What they treasure most. Come up with a new one any time I am stuck creating charachters. I totally stole this idea from the RPG game cyberpunk and their random roll charachter chart.
Look at your characters. Observe how they dress. Question why they dress like that and go farther with it. What's their personality? Why do they behave that way? What do they like, and why do they like it? Stuff like that helps me a lot when writing backstory.
You don't need a backstory, because that's the easiets way to get into what my teacher calls "bottle-neck", meaning you have all the information but can't get anywhere with it. Don't worry about writing something the reader will never know. Write more or less a sort presentation fo your character and leave it at that and then trust your story to write itself.
All you need to make sure off is that there's a red-thread with all these time travel and if it is directly connected to the plot. I would try to write each point in time as their own seperate event and make sure it's all connected to the plot.
For refrense, try watching movies like "Interview with the Vampire"(I am sure there's more but that one came to mind).
I find it easiest to start from their role in the story and what they do in the plot. The rest is fitting their inner life to what they do on and off work. It doesn't get easier but you can find methods of approach. Think you'll have more luck in Literature since this is a writing question.
Also check out the Writing Excuses podcast, it's rad.
Think of their motivations. If your character hates spiders figure out why they hate spiders. Were they bit as a child? Did they have an evil older brother who left a tarantula in their bed? Do they live in a world with mutant spiders that are ten feet tall? Did they create an army of robot spiders that turned on them? If they have blue hair, figure out why. Is it natural? Is it their favorite color? Did someone switch out their shampoo? Do they have some weird medical condition? Are they an alien?
Here's a quick example using one of my boys. His current name is Nishit Lyulf Smith. His birth name was Richard James Smith. He changed his first name to Nishit (technically it's spelled Nishith, but he dropped the H on purpose because he was kind of an asshole at the time...) because it means midnight, and that was his best friend's favorite time of day. He changed his middle name to Lyulf because it means "Fire Wolf" and his dead mother loved wolves and his dead younger brother loved the color orange (which is also why Nishit dyes part of his hair orange). Nishit is pretty much terrified of cars, especially military type vehicles such as Hummers and Jeeps, because he was injured fighting in Iraq when his vehicle went over an IED. There's more to his backstory, of course, but this is just a quick little example of what I'm talking about.
I think that the background should be related to the character's personality. Example: A quiet and lonely man, in the past he saw his family being murdered; An arrogant person, he was very rich during his childhood and had someone to do everything for him. About getting inspired, usually the BG I come up with for my characters are inspired by something I saw in an anime, movie, book, whatever.