Star Trek help needed!

Judith asked to watch "That programme that Daddy sometimes watches, and it's in Space, and it's on television" and amazingly I worked out she meant Star Trek (she did, the reason it was on her mind was because B was looking at Star Trek stuff online, only she wanted to watch it on TV).

Where's the best place in Star Trek to start off a dinosaur-obsessed 4 year old super hero?