For starters, Spider-Man is the only superhero, no other heroes available, but references can be made to locations like Wakanda, materials like vibranium and adamantium, characters like Stark & Storm, comic readers could get nods to them here and there, but no Iron Man or cosmic stuff
Costume would look somewhat different, gloves are shorter and the web shooters would be thin and made inside the glove, they are flexible to put on and off, and the material is strong enough to handle the constant bending even when it's fully stuffed. To attach the web shooters the gloves can be open like the mask in the Raimi movies
Origin would be decompressed, could take two or three episodes. Peter gets bitten by Oscorp spider injected by the Oz serum in the leg, Peter shrugs it off, and his luck is he's not under surveillance camera when it happens, so not something early for Norman to discover
Building the costume would be like the movies, thinks of designs and draws them, puts plenty of practical considerations before deciding the final look, and ends up with something notably different from the classic costume, but still retaining its main characteristics
The decision comes to take use of his newly found powers for his benefit, he goes to show biz, and a thief does pass by him, but instead of being arrogant or seeking revenge he pushes the thief back (cue from "What If Spider-Man Never became a crime fighter?" story) based on the good nature he was raised on by Ben & May, not controlling his strength he pushes the thief too hard and it makes him hit the security guy and push them both to the wall distant behind, Spidey becomes embarrassed and apologetic, but doesn't leave show biz, instead he tries to be more responsible using his strength if needed, and takes a chance in stopping small crimes on his way to work or heading back home
The thief eventually recovers, and does go to Ben Parker's house and kill him. When Spidey confronts him the burglar confesses about a stolen treasure he heard rumors about in that house, Spidey gets angry and punches the wall near the head of Carradine hard enough to make a hole in it, avoiding killing him in frustration, and giving him away to the cops
Rumors turn to be kinda true, but Carradine took the wrong house, the treasure is found in a neighboring house instead.
Spidey is quite experienced in holding back his strength, but that anger makes him leave show biz after a while on his own, deciding he should make more good use, thinking how many could die when he could do something about it in his spare time, educating himself in the line "With great power, comes great responsibility"