My only recommendation is DON'T. As you've seen yourself, relying on third party services is not a good idea, they can disappear at any time, fail, or just sell your data whenever they want. If you have something valuable, the cloud (ie, someone's else machine) is the last place where you want it.
Instead, save that money and buy an external HD or two, and place your backups there. It's a one-time payment, will never disappear and you'll keep full privacy at all times. Just make sure to handle them with care and have more than one copy of important data in case a drive fails.
An additional advantage is that you can simply delete the data from the main HD and use it direcly from the backup drive, without needing to download anything. You also save an immense amount of bandwidth.
I partially agree with you. While it is true that a cloud backup can disappear, be hacked, or sell off your data, it is far, far less likely if you use a reputable
paid backup
service rather than mere cloud
storage. The reputable cloud backup services would lose too much if they ever allowed themselves to be hacked or sold customers' data. Many, if not most, businesses use cloud backup services without a problem, sometimes even using one as their sole backup (the latter I do not recommend, btw).
The advice to not put your eggs all in one basket also applies to backups. All forms of backup media, be it the cloud, HDDs, optical disks, floppy disks, paper, stone tablets, etc., are subject to failure. For that reason, a cloud based backup should not be ones sole backup (although even that would be better than nothing). The same is true of HDDs; they are subject to failure whether they are the ones in your computer or ones that are external to the computer.
One's data is not reasonably safe unless it exists in at least three places, such as on the computer, on an onsite backup, and on an offsite backup (having all of one's backups onsite and nowhere is not a good idea, no matter how many one has). Using a good cloud backup service is an easy to use and maintain offsite backup but it should be used with a good onsite backup, such as on external HDDs for one's data to be reasonably safe.
Depending on how much data one has, an HDD might be cheaper than a basic cloud backup plan but HDDs are not a onetime purchase. HDDs don't last forever. They can last for years or they can fail almost immediately. Eventually, they will need replacing. I use a Carbonite.com basic plan and it costs only $60/year (actually, it cost me a bit less since I signed up for a multi-year plan at a discounted price) and it allows unlimited data storage. Unlike a single HDD (or even multiple HDDs used individually), cloud backup services use layers of redundancy and keep their servers in secure buildings with backup systems, such as air conditioning and backup generators, to considerably reduce the chance of data loss due to equipment failure. The good cloud backup services also have business plans (at a higher cost, of course) have geo-redundancy. In other words, data is stored in multiple servers that are in locations that are widely separated from each other by hundreds, if not thousands of miles.