So the MC could be reincarnated and given Spider-Man powers or the MC could have been born in the MHA world and was bitten a spider or was chosen to be Peter Parker's successor.
You could make the MC a genius just like Peter was.
Have a training arc, where the MC gets used to his powers and works to improve his body.
You can also have a chapter where he invents devices for his costume along with costume itself.
Even before the MC makes it to UA you would want to make him go out and fight villains as a vigilante, the friendly neighbourhood spiderman.
For the costume design please use the Black Spiderman costume from the cartoon.
(A/N: Here's a pic)
Since vigilante work is like literally illegal in MHA you can have him be caught and forced to either attend UA as a student, intern or maybe even as an instructor.
From here on you would want to follow the main storyline while injecting our MC in the process.