Dolly Drive comes to mind. My understanding is they offer exactly what you want, although you'll have to double check if they do it in a manner that suits you. They do offer a fee trial, but this is limited to 100GB - so it probably won't allow you to test it properly for your purposes.
Since you mentioned using a virtual private server, you could do this without the need of purchasing any extra software. You will, however, need access to a VPN you can use (usually at a monthly or yearly cost). This option also requires that you understand how to use SSH (to run commands, and to edit files). If this is something you're comfortable with, you can check out Configuring Time Machine to back up to your own server over the internet
Another possible option is to just use
rsync to regularly copy your data to a cloud service. Rsync is a Unix tool to synchronise data between disks or servers, and it supports incremental updates. This option, of course, requires you to be willing/comfortable to use Terminal. As a starting point you can launch Terminal and enter the
man rsync command for details.
I'm sure others here will have suggestions for you.
My personal view
You can choose to ignore this little blurb, otherwise read on. :)
My preference is not to use the cloud for this type of backup. The cloud is great for low volume data storage and file services (e.g. Dropbox, iCloud, Google Drive, MS OneDrive, etc), but for this type of backup it's not (at least not yet). And, in terms of the OS you can always restore macOS directly via Apple online.
My recommendation to users is to always alternate two TM backup drives and store one of them offsite. By way of example, I'll explain how I do this for one of my Macs (but I follow a similar process for all my machines!)
- This iMac has a 500GB HDD
- I have purchased two portable USB 2TB external hard drives
- I have labelled these hard drives as iMac TM Backup HD 1 and iMac TM Backup HD 2
- I set both of these external drives to be TM backup drives
- As both drives are set up with TM they are alternated whenever both drives are available
- Once the initial backups are done, I physically remove one of the external drives and take it 'offsite'
- On the same day each week, I then swap them over
- The net result is that both hard drives will have backups in the order of one week on, one week off (but between them I have a full set of backups).
Now, in terms of keeping one of them offsite, you have a number of options. Over the years I have used as my offsite location any of the following:
- My workplace
- A shed in the back yard
- My car (but this may depend on your climate and where you 'garage' your car)
- A family member's/friend's place (assuming you trust them!)
Basically, the idea is that your offsite drive is somewhere that protects your data in the event your house burns down or you get robbed. My strong suggestion would be in a locked drawer at your workplace (unless you work at home). Most people's workplaces are air-conditioned, secure, and convenient.
Regardless of the 'offsite' location you choose to keep your hard drive, there are some key factors to keep in mind:
- Always keep the drive safe from large magnetic fields!
- Ensure the location has a temperature range between 10 degrees celsius (50 degrees fahrenheit) and 43 degrees celsius (110 degrees fahrenheit). So, keeping it in a car would usually not be a good idea.