Also, you should consider approaching canonical about sponsorship. Considering their relationship with amazon there has to be some funding to be found there.
I think the OS choice also reduces the hardware cost a little bit -- at least windows laptops usually have a bit more hardware to support more standard interfaces. Some of the Chromebooks have i2c keyboards, which I don't think passes WHQL standards, but must be a little less expensive; the ssds are tiny, and sometimes mmc which is slower, but less expensive; the keyboard have fewer buttons which reduces cost a smidge too.
But, more importantly than the hardware cost, Chrome OS is easier than Windows for a novice to manage -- updates are less intrusive, just reboot when it asks and wait about 10 seconds to be ready to work again. There's not as much to mess up, and when you do, it's usually easy to get back to factory fresh.