It's hard to tell what exactly you need because I'm not sure of your use case. I mean, as far as your daughter needing one for school, I think you should put a lot of weight on the battery life of whatever laptop you end up getting. In fact, in my own buying decision battery life was almost the single priority I had, so I bought an
Asus Eee PC 1000HE, a netbook that gets about 7 hours of battery life. If you don't mind buying a netbook (which typically run pretty low on the power/performance side of things, but keep portability and battery life in mind), Asus has an updated version called the
Eee PC 1005HA, which weighs a little less than three pounds, gets about 10 hours of battery life and has a 10" screen. Also, keep in mind that since you're sacrificing power for portability, the prices on netbooks typically run quite low, that particular one going for $330.
Now, with the assumption that portability is still a priority, the Acer Aspire Timeline series will give you a little more
oomph! while keeping price low and battery life high (~8 hours). The screen size of the Timeline is also a little more usable, usually running between 12" and 15". The
Acer Aspire Timeline 1810t has the svelte design of an ultraportable laptop, packing an 11.6" screen and noticable upgrade from netbook processors and integrated graphics chips. The
Acer Aspire Timeline 3810t knocks down the price a tiny bit and packs a larger screen, if 13" is more your preference.
Finally, if you want a compact, portable laptop but you really want some performance, the new
Alienware M11x is actually affordable and packs a solid punch. I've actually been lusting after this sonovabitch for a little while now, but it goes for $800 starting price and performs like a gaming PC. With graphics switching to optimize for performance, this laptop can get 8 hours of battery life when doing light tasks like web browsing or word processing. When you want to watch HD videos or play 3D games, this tiny titan can tackle anything by switching to a more powerful graphics card. And best of all? The laptop packs a 11.6" screen, small enough to fit in the smallest of bookbags.
Now, those all kept in mind the idea that smaller screens, high battery life, and portability were a priority, but if you want desktop replacements or don't mind 15" screens, there are tons more options. Either way, you should probably more clearly define exactly what you want to do with the laptop, which will make it easier to figure out what you need.