Oh boy.....my DD grandmother bought my kiddo her first one and at 13YO, she now has over 30! Good Luck with this! Ha Ha Ha
To make it easy for you, I consider AG to have 3 lines.
The numbered ones which most girls start with getting one they this is simply pretty or looks like them.
The named ones, which all come with a story (they include books and their own line of merchandise)
The girl of the year ones. A special doll available only for that year (and of course into the following year until they sell out)
As you already know, these are not cheap. You may want to simply ask her "what is an AG doll" and pull up the website with her as more of an education for you, while secretly finding out which one she desires.
Now...for discounts. Yes, sign up for their mailing list. Sometimes you will get lucky and get a catalogue with 20% off coupon. If not, go by one on ebay or another coupon site. I usually pay around $5 for them - but make out in the end.
If you shop in store and know someone with a military ID, bring them along. They get 15% off.
Lastly, there is an AG outlet store in Hershey, Pennsylvania that has pretty good prices. If you are lucky enough to be in that area, it would be worth the trip (especially for accessories)