I think, for the sake of the plot of the movie, it made sense to create a connection between Peter and Tony in order to find a way to justify him getting involved in the Civil War conflict, and obviously they wanted a more plausible explanation for the high quality look of the Spider-Man suit then what you would expect a teenager to pull off (because apparently suspension of disbelief only goes so far on that subject).
That being said, I'm personally not too crazy about it. I think Peter works best as a self-made hero without any "upgrades" or "tech" from somebody like Tony Stark, and doesn't need any kind of mentor to be a hero, least of all from someone like Iron Man. Maybe this stretches disbelief, but we're already dealing with a character who stretches things enough as is, especially when he actually has a secret identity (and those are apparently so unbelievable).
And I don't think Spider-Man on an Avengers team has ever been very noteworthy outside the novelty of it and a few significant but far between character moments. He's really only their for comedy relief and quips and that's it, rather then actually contributing something worthwhile to the group.
It's like on the Ultimate Spider-Man cartoon, in emphasizing Spider-Man in a team setting and working with SHIELD it feels like a lot of the essential elements of Spider-Man have been lost in the process or marginalized, because it's not a natural fit for the character.