Altium does support version control. Some people use it, I tried it, but it didn't work well for me. I do not really need to go back to previous versions (if I do big changes, I simply zip the whole directory and mark it by date). What I use is a NAS server (with double harddrive) + automatic NAS server synchronization with google drive. I have to say, I regularly use versioning system (e.g. github) for software development and other files, but I have not really found it very useful for schematics or PCB.
PS: I used to do backup on external harddrives. Then I decided to buy NAS (I have simple TS-453A: https://www.amazon.com/QNAP-Professi.../dp/B017YB7T6U
). When I bought the NAS server I was like - I should buy it long time ago - it's so good. You will need to add price for hardrives, but it is worth it. I run two 2TB mirrored (doubled) hardrives + 8TB hardrive. One slot is empty in case I need it. On the mirrored harddrives I store the most important every day work, on the 8T I store the files which are not updated so frequently. The mirrored harddrives are synchronized with google drive (in case of fire or something really bad happen in our office), the 8T hardrive is backed up once a week to Amazon Glacier (cheap archive storage online).
PSS: However, if your client has very special requirements e.g. no cloud, then you may want to use NAS and other approach (e.g. another NAS on different place or external storage which you will then keep outside of your office).