Peter is likely to be in awe. He might be a bit nervous at first, but also extremely excited. He has looked up to the Avengers for a long time, so meeting them would be like a dream come true. He would probably be stuttering a bit as he tries to introduce himself and show his respect.
Peter's reaction would be complex. He's a big fan of the Avengers, so he'd be overjoyed to meet them. However, he also has his own insecurities. He might worry about whether he'll fit in or be good enough. He'd likely be looking around in amazement, taking in all the heroes in one place. His eyes would be wide with wonder, and he'd be trying his best to act cool and composed, but his excitement would be hard to hide.
He might also get angry. Peter has a strong sense of justice. If he feels that the Avengers are being unfair, he could stand up to them. He'll use his quick wit and his powers to show that he's not going to be pushed around easily.
Peter might be really nervous at first. He's used to being just the friendly neighborhood Spider - Man, and now the Avengers know he's Tony's son. He could be worried about living up to their expectations.
Some fanfics show the Avengers being protective of Peter Stark. If he's a young and inexperienced character, Thor might take on a big - brotherly role. He could offer to train Peter Stark in combat or share his knowledge of different worlds. Iron Man, if not related to Peter Stark in that particular fanfic, might be a bit jealous at first of his intelligence but then realize they can work together for the greater good.
Tony Stark might use his quick wit and technology. He could immediately scan Peter to make sure there's no physical danger causing the hyperventilation. Then he'd probably crack a joke to try and calm Peter down, like 'Kid, you breathe any faster and you'll fly away like a human jetpack.'
Peter might be very defensive at first. He could argue back, trying to explain his actions. After all, he is a teenager with his own ideas and he may think that the Avengers don't fully understand his perspective.
The Avengers might react in different ways. Steve Rogers would probably be polite but firm in getting to know Peter's boyfriend. He'd want to ensure that he was a good influence on Peter. Thor, on the other hand, might be a bit more boisterous. He could either be really friendly and enthusiastic, or his loud and powerful presence might accidentally scare the boyfriend a bit.
Some Avengers might be initially shocked. For example, Steve could be a bit taken aback as he tries to understand how this could be possible. He might be concerned about the implications for the team dynamics.
It could be a really exciting and unexpected encounter. Maybe Howard is shocked by Peter's abilities or they have a deep conversation about the future.
Maybe it's a tense meeting with lots of misunderstandings and later resolutions. Or it could start off awkward but end up with a mutual understanding and respect.
Natasha Romanoff could show her emotions in a more subtle way. She might look at Peter's old things and a small smile would cross her face as she remembers his innocence and determination. Thor, on the other hand, might become more determined to protect the world in Peter's honor, as he respected Peter's strength despite his young age.