This depends a lot on you and the girl,... So obviously on your first date you should concentrate on getting to know the girl. I think a safe bet on the first date is to end it with a hug. If she shows obvious signs of wanting more, you may consider it, but it's not very likely, specially if you describe her as shy.
If she is really very shy, then really do the hug at the end of the date, so that she starts to get used to physical contact.