She goes home to her family. He goes after her.

She fell in love first. I'm not sure how far this is a valid point, since Shang thought she was a man for most of the movie, but I'll go with Mulan basically because we are able to see more of her feelings development than Shang's.

All "Shang is gay" jokes aside, he realized his feelings when he found out she was a girl. She, however, was very aware of her feelings, even if she denied it to Mushu. While they may have been falling in love at the same time, Mulan was the only one aware of her feelings.

^ Ditto what Tygers_Eye said.

^

@Tygers_Eye: Well, Shang goes after Mulan only because the emperor "commands" him to go after her implicitly by saying "You don't find a girl like that in every dynasty." It's not because he really intends to. XP

Mulan is the one who likes her by continuing looking at her and Mushu recognizes that and teases her that she loves Shang.