Shared File Storage in the Cloud

Hello

I'm a high school teacher who teaches video production and my school would like to do away with our local file server for budgetary reasons. I'm trying to find a viable solution where students can still save files, share them, access them at the same time and build their video projects with Premiere Pro & After Effects that is cloud based. Obviously I don't want to slow down our work flow, I don't want any play back lag and I don't want to deal with dropped files and lost projects.

Amazon Cloud didn't work well.

Does anyone have a solution to this problem?

Please help!

Thanks you!