There has been no lack of Spider-Man movies over the last couple of decades which means there is very little new and different for Spider-Man: Homecoming to do. Instead, it appears the MCU version of the character will try to differentiate itself by what it avoids. In this case, what you won't see in Spider-Man: Homecoming is a web slinger that swings across the top of New York City from impressive heights. According to Co-producer Eric Carroll, this version of Peter Parker will be lacking the confidence to be that high in the air.
Spider-Man starting out -- he's not irrationally afraid of heights, but he has the fear of heights that all well-balanced people do. So he's going to work up to becoming the Spider-Man we know he will someday. But we will not see him swing down Fifth Avenue in this movie. We will not see him 40 stories off the ground acting like that is not the most terrifying thing he will do that day.
Our own Sean O'Connell got to visit the Atlanta set of Spider-Man: Homecoming where Eric Carroll revealed that this new MCU Spider-Man is still getting his bearings as a hero and so he won't be the kind of Spider-Man who swings from the tops of buildings in New York City like it's no big deal. If we do see him high in the air, it will be in a situation where Peter Parker is very conscious of the fact that he's really high in the air. And even the least acrophobic person is going to be concerned about literally hanging from a thread from a significant height.
It certainly makes sense. Even in the online videos that Tony Stark showed to Peter Parker in Captain America: Civil War we only saw him just above street level. As Eric Carroll point out, most people have at least a basic fear of heights. It's not necessarily a phobia, but most of wouldn't be comfortable enough to just start climbing to the top of skyscrapers. While we don't really know exactly how long Peter Parker has been out there fighting in his homemade suit, the implication is that he's still fairly new on the scene. While he clearly has a handle on his powers, he probably doesn't have a handle on their limits, and who wants to discover they falter at altitude while actually hanging hundreds of feet in the air?
The other thing that's interesting is that based on this comment, it sounds like we won't necessarily see Peter Parker 40 stories up at the end of the film any more than we will see him there at the beginning. Eric Carroll says that he will become the Spider-Man we know "someday" which would imply that we'll be seeing this transition over the long term, likely over a handful of films.