what color should i ask for if i want this:

I've never really watched Gilmore Girls, but judging from those screencaps, I'd guess that her haircolor is approximately a mahogany brown. That's basically a dark brown with red undertones.

Like what the previous poster said, check hair magazines for something similar. There's lots of "celebrity" hairstyle mags out there and she ought to be in at least one of them.

You can look at the magazines in the grocery store and find someone else in one with the same haircolor, then bring that picture to the salon.