Cloud backup and also remote access to files

I want to have a cloud backup of the files that are on my new MacBook Air and also to have them available to me when I am not home. My MBA has a 256GB hard drive and I have 300GB that I want to have backed and available to me wherever I am.
Should I invest in a server at home and have those files backed up to a cloud storage backup? I look forward to any other suggestions.

Thank you for looking.