As far as size goes, my Dell is a 15 inch and I didn't find that it was too big or heavy. It was about the same size as a textbook and I didn't have any problems carrying it around UT's campus, which is pretty big. I would recommend that, whichever size you ultimately get, you get her a neoprene sleeve to put it in, which will provide a little extra cushioning when she puts it in her backpack, but not take up too much room.
I don't see any need to bring a desktop computer in addition to a laptop. One or the other should be fine and having two computers just makes you worry more about something happening to one or the other.
Also, this is just something to consider, but if your daughter is thinking about studying abroad, it may be worthwhile to explore how the warranties work overseas. I got my Dell lappy before I went to Australia for a semester and decided to get the in-home service warranty so that if something happened while I was in Australia I could get it fixed locally rather than having to mail it back to the US and then have it mailed back to me in Australia. Anyway, if she might study abroad, I would look into how the warranties work overseas.
