Let start with the biggest drawback of a chromebook, that may actually be a good thing for parents. They cannot run Windows programs, meaning you can not install software that isn't offered in the google store. This makes the chromebook unusable for someone who needs to install software for work or school but also adds a level of security as a parent. You won't have to worry about your child installing a malicious software that can compromise their personal information. Also, although malicious websites are still a threat, the google store offers free high level security programs to prevent infections.
The cost of chromebooks has actually gone down in recent years. The cheapest will run for $150 and the most expensive ones can exceed $500. The Toshiba CB35-B3340 Chromebook is one of the best chromebooks available and the one I use personally. It is lightweight but extremely powerful and can complete any task I throw at it. I actually transitioned to using this computer over my standard laptop, due to its fast speed at loading websites.
If you are looking for the best computer gift for a teenager, I seriously recommend a chromebook, available through Amazon.com and other retailers.