If you want good storage with great synchronization support for Linux, you can try any of the following cloud storage services for your data:
The above 3 are very popular and have Linux Synchronization clients that make it easy to synchronize selective data with the cloud. Files can also be accessed on any other devices like Android phones, tablets, windows or Mac computers.
I cannot mention Google Drive in the above list, because it simply does not have a good client that works with Linux. You can use synchronization utilities or programs like Grive or google-drive-ocamlfuse, but they are too slow and too involved, to make any practical sense.
Of the above, SpiderOak and mega.co.nz state they support zero-knowledge encryption, where whatever data you store on their servers is not visible to anyone except the person who knows the password. Copy.com does not allow you to purge the recycle bin, but they do it at periodic intervals for all accounts.