I'm using Google Drive: google.com/drive/download/
You can install it on your machine and it makes sure everything is synced between your computer and the cloud. I have set it up to only sync some (most) folders and I have one backup folder in the cloud that I don't have on my computer. All the stuff I use/need on a day to day basis is being synced between my computers and Google Drive, the back-up folder I use for storage.
Compressing video can surely be done on your computer. Have a look at VLC player:
Then just google something like "compressing video with vlc player"