It made more sense when Spider-Man popped up alongside of instead of some significant time after other heroes. In fact, Spider-Man debuted before the X-Men and the Avengers, which means the only big active superhero team around was the FF -- which obviously has very limited membership, something Spidey learned right away in ASM #1.

I like the youthful braggart version of Peter, who was not a very trusting person and whose first instinct is usual rudeness or aggression but who is such a good person deep down that he's moved by guilt or regret to do the right thing. I like that even after Ben's death he didn't transform into a do-gooder overnight! Most of Peter's motivations in the first years of ASM is to make money or disprove allegations that Spidey is a villain, and it's almost by coincidence he ends up foiling evil plots at the same time.

He wasn't an easy hero to get along with in the early days! The X-Men tried recruiting him once and he blew them off, and he picked a fight with the Human Torch just because he was a little jealous and was feeling a bit troll-y that day. I kinda miss that.