Write a little program in your favorite shell or scripting language that * rsyncs the directories containing the files you want to back up * mysqldumps/pg_dumps your databases * zips/gzips everything up into a dated archive file * deletes the oldest backup (the one with X days ago's date) Put this program on a VPS at a different provider, on a spare computer in your house, or both. Create a cron job that runs it ever…
I've used it for many, many years. Setup is a bit of a pain, especially if it's your first time, but it's a totally reliable backup system and gives you something much better than just a pile of zip archives.
All of our servers get BackupPC'd (rsync-over-ssh, pulled) twice a day to an in-house server that's totally unreachable from the internet. I get emails from BackupPC when something goes wrong, which is pretty much never. Backups aren't a thing I have to worry about much anymore.