If Marvel was ever thinking of doing a new Marvel Team-Up — and doing it the right way, they ought to have the book star The Thing, not Spider-Man ... yeah, The Thing!
As a superhero who routinely faces cosmic foes, he's tough, but he's not all so powerful that he could be bested by even a weak foe. Also, unlike Spider-Man, he has the means and reason to travel the globe as need be. Additionally, he isn't oversaturated like Spidey.
Now if we were talking about setting up a Marvel Team-Up style book over in the DC Universe, I'd go with Captain Marvel. He's tough, but naive at times. He has a mentor that can direct him to places of crisis. Also, unlike Spider-man, Batman or Superman, he's clearly not oversaturated either.
As a back up choice, I think Blue Beetle (even a non-joke cracking one) would be a good choice. He could be directed by Oracle. He has all the free time he wants and he has coolest ride in the DCU.