Steve Rogers wasn't doing anything important during his first encounter with Spidey.
He was just walking down the busy New York streets trying to find a hot dog stand. He was hungry. All of a sudden, a red blur whizzed down from the building on his left across the street. The blur knocked into him, sending his flying forward a good five feet. Steve fell flat on his stomach. The blur, which had solidified into Spiderman, rolled elegantly to a stop.
"What in the world?" Steve asked before he heard a crash behind him. When he turned onto his back and sat up, he saw that a lamppost had fallen to the ground. If he had been a regular human, it would have killed him. Even as Captain America, he would have felt considerable pain.
"Are you alright…..." Spiderman trailed off as he realised who he had just saved. "Oh God! Captain America! I'm such a big fan and I just wanted to ask…." He paused as he realised Steve was still on the ground. He put out a hand to help the Captain. Steve gratefully accepted and was surprised when the Spider was able to pull him up.
"What are you doing in Queens?"
Steve laughed.
"I'm looking for a decent Hot dog."
"Oh! I know this great stand. If you take a right at the next lights, then a left at the next intersection, you should find it." Spiderman answered, "Spider out!". He gave a mock salute and disappeared into the sky.
Captain America was left staring at the sky and wondering if that had really just happened. He pulled out his notebook and added something to his list: Spiderman.