I don't mean "sitting down to write", I mean the literal beginning. The story itself starts with my protagonist running. I need to get him to run, then I'll have the rest of it sorted. But won't starting with "He ran" sound cheap? Should I add something before? Or should I just go straight with "He ran. This and that happened, so now he's being chased"? Or maybe it would be better to start with describing "this and that" and then progress to the running sequence? The "this and that" wouldn't have much to do with the story, so I worry whether it won't be just a filler and won't bore the reader. That's what I'm worried of the most, that I would bore them before anything would start.
The first part of a book / story should almost always be the normal life before the event that really pushes the story forward.
If you don't want to do that, you need to ask yourself why he's running. If he's running for a reason (emergency, he's in danger etc.) then "he ran" is absolutely fine.
You can also decide how much information you want to give at this point. Saying something like "Looking over his shoulder again, he ran. His breath, laboured as he struggled to fill his lungs while his suit jacket flapped around him." You reader knows he's running and he's scared but doesn't know what he's running from. Or towards.
Equally, you could start the book where he doesn't want to run (over did it at the gym last night and his legs are really hurting today?) but by the end of the chapter, something else has happened that means you can end that chapter with "he ran."
The opening lines generally set the tone of the book. Why are you starting with your protagonist running? Is that the theme of the story, are they running away from something physical or emotional?
Take the first line from Pride and Prejudice:
"It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife"
That is indeed the main motivation of Bingley, Mr Colins and even Darcy and Wickham. It's also the preoccupation of (most) of the female characters. The opening line sets the expectations of the reader for what is going to follow.
So my answer is to think about the overall theme of your story and write a beginning that informs the reader of the journey they are about to embark on. The art is doing that without being blatantly obvious about it.
You don't have to just say "He ran", your opening sets the stage for where the action takes place and gives us insight into the character. You can state things about the environment, what the character is thinking as he is running, what the character looks like or what their background may have been like before they had to run.
Shadows danced over the graffitied walls and dumpsters of the alleyway as he ran past streetlights and illuminated windows.
It seemed as though the shadows themselves were chasing him as he ran through the graffitied walls and dumpsters of the alleyway, no matter how fast he ran the shadows kept up.
His tailored suit flapped wildly as he ran along the graffitied alleyway, his slicked back hair disheveled from his frantic running.
Lots of fine answers here, and as many good choices for you. Starting with the running is great stuff if that's what your book is about. 'In medias res' is the formal phrase for it, and that tells you how often it happens.
But don't underestimate the moments before the running starts. It doesn't have to be boring, it can definitely be used to ratchet up the tension. Maybe he spots one of his pursuers, but he doesn't know what the others look like. He tries to blend in with a group and casually exit, but then runs into the partner.
Or maybe he's part of a group watching a dead-drop to see who collects the bundle of cash, and he's on the coms with his own partner. Then a maintenance truck blocks his view of the park bench, and by the time he gets through a crowd of people, the backpack is gone. He spots two people running in different directions!
The point is, the reader knows weapons are about to be drawn, and the running will start any moment. You have a chance to define good guys and bad guys, and display a bit of your protagonist's personality while building tension. You're just tightening up the spring until it snaps and the running starts.
Disclaimer: this answer relies on my own experience and may not fit your needs.
If you story starts with someone running, then there must be a lot of action later.
Even if it's wrong, this will be the first assumption of the reader while reading it. I will not go in detail about this because Matt Hollands' answer is already covering it pretty well.
The same way, if you begin a book setting a date, let's say "2014", you unconsciously know the story will stretch on months or even years. But if you start with "monday", your whole story won't probably last more than a few days, which set different expectations to the reader.
If you begin In Medias Res, start answering question early instead of piling them.
Years ago I wrote a series of short stories that somehow get published in a small magazine, and the first one literally started with "He ran" ("He" being the name of the protagonist).
At the time, my litterature teacher told me it worked because within the next sentences, I was explaining the threat from who he was running from (who was after him and why), and the setting which was important for the rest of the story (empty streets after a curfew, troops of Guards looking for offenders, wanted posters with his face on it, etc.).
The important thing here is: your "this and that" must not be a filler. If your character is running, there is a reason for it and your firsts paragraphs must expand on that reason. If it is unrelated to what follows in the story, then your MC running may not be the good approach.
Then, when the threat is gone temporarily, the protagonist may rest and have a flashback about how he got there (probably not the best follow-up, but that's what I did at the time).
Now the whole "You probably wonder how I got there"-flashback thing may sound silly, but it is exactly what you see or read in most of action movies nowadays. It is the stinger, or the hook of the story. A little digest of what could happen later: action and mystery. Your "hook" reflects what the reader will find later in the book; if the reader adhere with your first chapter, you already know he will read the rest.
My suggestion is to view your story like it's a movie. Imagine they're not reading, but WATCHING. How do you want your readers to visualize the scene? If you start the story in Media Res, put MC right in the middle of the chase scene, and really zoom into the action- he's jumping over an apple cart, apples are flying everywhere, he landed in a crate of pears, the vendors are screaming- but he can't stop! Then zoom out later when the action dies down and explain what happens.
You could also do a POV shift: tell your readers about what's going on by placing them next to someone telling the story- the bad guys, for example, explaining what they're gonna do to MC when they catch him, finally getting their revenge for that time when he did XYZ- then pan back to MC.
Or, you could do an alternating sequence, either with MC before the chase in a state of calm alternating back and forth between this and the chase, or with MC after the chase in whatever state he's in, alternating to the chase.
In essence, just play with structure! There's no reason for things to be in order if the reader will figure them out eventually!