Straight no Chaser

Shuuhei is an endlessly enthusiastic pizza deliveryman with almost no ambitions or skills, and he's determined to date Hitomi, a high school girl who made the mistake of kissing him once. Her disinterest can't stop him from loving her, though! When he asks her what she likes in a man, one of the things she mentions was the ability to play a musical instrument. In response, he decides to learn to play the trumpet. But learning about the trumpet and jazz music is going to change his life in more ways than he imagined...

(Source: MangaHelpers)