I want my Spider-Man to be competent.
I want my Spider-Man to be able stop bad guys and fight crime without needing a sidekick, supporting character, or guest hero to have to bail him out on a consistent basis.
I want my Spider-Man to be clever and able to come up with smart plans or creative uses of his powers.
I want my Spider-Man to be smart and intelligent but not necessarily to the same extent as Tony Stark and Reed Richards.
I want my Spider-Man to have the emotional maturity of an adult.
I want my Spider-Man to be pretty strong, but not to an absurd degree.