To me, the pieces fit together perfectly, and sensibly enough:
Hank Pym is an older scientist, say in his 50s now, who discovered the "Pym particles" back in the 1980s and figured out how to miniaturize himself as Ant-Man. He gets tired of the cloak and dagger stuff with SHIELD, though (he's essentially a hippie peacenik), and drops out of spycraft.
Fast forward to the 2010s, and thief Scott Lang breaks into Pym's mansion (provided to Hank in a generous retirement package by Nick Fury, courtesy of the American taxpayer), steals some stuff, including the Ant-Man suit. Lang becomes the new Ant-Man, and Pym eventually warms to the idea (mainly because of the ol' tugging heartstrings story about poor little dying Cassie) and winds up mentoring him.
Janet Van Dyne, Hank's hot younger girlfriend, catches wind of what the two "Ant-Men" are up to, and wants a piece of the action. Hank is reluctant, but Janet is too strong-willed for him to refuse, so he uses the miniaturization on her in a risky procedure that somehow requires both him and her to be part of the experiment. The experiment is, well, successful, but not necessarily in the way Hank intended: Janet miniaturizes all right, and becomes the ever-lovin' Wasp; but the Pym particles reverse in *his* procedure and he actually grows to giant size. Enter: Giant-Man.
So our three amigos --- Giant-Man, Ant-Man and Wasp --- finish the movie with a climactic flourish; Fury talks Hank into coming back into SHIELD; Janet and Lang want to come, too. Avengers 2: Giant-Man, Ant-Man and Wasp join the roster.
It's simple, elegant, and even slightly faithful to canon.
But.....yeah, it's a pipedream. And I'm sure Wright doesn't give a damn about how the pieces fit into the Avengers. He's telling his story, and canon and continuity be damned.