In the first one I believe Kurt ends up skipping a grade. Finn introduces him to New Directions and everyone but Rachel takes a liking to him. Rachel doesn't like the attention Kurt is getting and quits. Don't remember much more other than Puck and Kurt start dating.
In the squeal everyone moves into the same apartment building in New York. I remember Puck is in police academy. Rachel follows them and causes trouble by sending letters and pictures, breaking into the apartment, and ends up getting arrested.
(sorry about any missing tags. This is my first post)