Rose

Original BBC Website: Episode 1

"Nice to meet you. Run for your life!"

This isn't the best episode of the series. In fact, it may be the least best episode. But, it successfully introduces the characters and tells you as much as you need to know to get started.
The plot is kind of tacked on and the enemy is a 1970's retread. If your attitude toward this first expository episode is "meh," episode 2 is probably a better exemplar of the show.

One last observation: If your boyfriend is replaced by a talking mannequin and you don't notice, it may be time to find a new boyfriend.