When you buy from a
KEH,
Adorama, or
B&H the store is the seller (it's not like
EBay where the store is just facilitating a transaction). They "grade" the condition of the equipment and they are reliable (if they tell you it's in like-new condition, it really is in like new condition. They'll also tell you when it's so badly beat up that it's probably only good for spare parts.) However... since they bought it and trying to maximize their profit, they picked it up from the seller at a lower value than the seller could get on their own, and they'll resell it for a higher value then you could get from a private seller. They "know" what the lens is worth and will hold out to get that price. You'll pay less than you would for "new" but you'll get a better deal from a private seller.
The catch is that when you buy from a private seller, you have to be concerned that they are accurately representing what they are selling. Does the seller know what to look for? Do YOU know what to look for?
Another possibility is to buy a "refurbished" camera. These are cameras that were returned, reconditioned, and sold WITH A WARRANTY.
You didn't mention what type of camera you have, but I'd suggest you buy your daughter the _same_ brand. This makes it possible to pool your resources for things like lenses, flashes, etc. so that you don't both have to buy what would amount to the same lenses because they're for completely different camera systems.