Having only recently put hands on an Academy Series guitar for the first time, my impression of it was largely positive for the market segment at which it's aimed: namely, first-time players. Now that the current 100 Series has transitioned to a body using a Walnut laminate, the Academy Series is perhaps best thought of as a 'legacy' 100 Series guitar (Sapele laminate) -- with a few extras like an armrest bevel (which is, frankly, little more than a strategically-angled and -tapered cut in the body that functionally mimics the more aesthetically-pleasing high-dollar armrest option that Taylor has offered for years now) and an onboard pickup with built-in chromatic tuner. So in my mind, the Academy and 100 Series guitars are essentially equivalent, with only some features and aesthetics providing the distinction. And they both sound fine.
200-Series guitars, to me, are 100-Series guitars with some upgraded aesthetics: different (more 'traditional,' perhaps more 'exotic') wood laminates like Rosewood and Koa with gloss finishes. So basically you're getting a prettier 100-Series guitar for you money -- the cost justification for which is left to the consumer. There's not likely to be a significant difference in tone between all these laminate-body guitars, though...
The GS Mini is definitely a great little guitar, but in my mind it's really in its 'sweet zone' when employed as a travel guitar, not as a primary guitar. And given the miniscule price difference between it and the Academy Series, I'd personally lean more heavily toward the latter in a situation like yours.
But in the end it really boils down to: which guitar best suits your daughter and her playing style? Have her try them all and see which she likes best.
