I have been using Adobe Premier Elements, and really like it. It is a one time fee, as opposed to the Primer Pro standard package that hits you up for a monthly feel. It has 3 "modes" one can use it in with increasingly more detailed editing options. This could be good for students who might only need a handful of entry level features.The Resolve software is great too, but has a steeper learning curve in my opinion.
Editing on a Chromebook will likely be a challenge. Video editing requires lots of RAM and a good graphics card. Chromebooks are typically much lighter in the resources they have to offer (since they do not need them). Also, most of the programs listed are not browser based, and do not have apps. Perhaps others know of some that do. In general, it might be a tall order.