For storing the backups, I use a storage VPS. I got one from HostHatch a few years ago during Black Friday sales, with 10TB space for $10/month. Hetzner have good deals with their storage boxes, too - they offer 5TB space for $13/month if you're in the USA (you need to add VAT if you're in Europe).
A good rule of thumb is to never pay more than $5/TB/month, and during Black Friday it's closer to $2/TB/month. The LowEndTalk forum has the best Black Friday deals.
I use Borgbackup for backups, and Borgmatic to handle scheduling them. Borgbackup is a fantastic piece of software.
Borgmatic has an "append only" mode which lets you configure particular SSH keys to only be able to add data to the backup, not delete it. Even if someone/something (ransomware, malicious users, etc) gains access to your system and tries to delete the backups, they can't. Essentially, this is protection against ransomware.
This is a very common issue with other backup solutions - the client has full access to the backup, so malware on the client system could potentially delete all the backups.
I have two backup copies of most things. One copy on my home server and one copy on my storage VPS. If you do do multiple backups, Borgbackup recommend doing two separate backups rather than doing one then rsyncing it to another server.