I would check with the school first and see if they use a particular productivity suite (Office, Google Apps/Docs, iWork, etc). Make sure whichever choice you make is compatible.
If you are on a budget, the Chromebook is the way to go in my opinion. I suggest taking a look at the Toshiba Chromebook 2. I use one for my own work and have found it meets almost all of my needs. They are relatively inexpensive, fast, reliable and do all that most people expect from a computer. There are some drawbacks, though; unless you have a Google Cloud compatible printer, printing is a pain. Also, you can't really install software (there are some offline apps), so if you don't have a WiFi connection the usefulness of a Chromebook is very limited.
On the other hand, a Windows laptop is always a decent choice. It can do everything the Chromebook can do, especially if you use the Chrome browser. It can also run the huge library of Windows software, and that is a significant advantage. On the downside, a decent Windows laptop is going to cost at least $500 (note that we may have different definitions of decent), almost double what a good Chromebook will cost, and more than double what an acceptable Chromebook will cost.