For the stated goals of writing a custom local backup, I'd use a bash or zsh shell script and launchd, or would use periodic. Among other uses, I've a script summoned by periodic for a similar task; for some database backups that Time Machine can't otherwise get a reliable backup of.
You will be using cp and rm commands, here. Also handling deleting the older backups, and that deletion preferably after the new backups are created. (Coincidentally, I posted a zsh script here that fetches the dates from files and uses that as the filename a day or so ago.) I'm certain there are example backup scripts posted around, but have not gone looking for those.
Treat rm with great care.
Double-quote all file specifications, as spaces are likely.
Building the launchd plist can be a little involved, and the Lingon app can help there.
For info on periodic, see man periodic.
Launchd is more flexible, while periodic is brute-force and tends not to be all that great about error feedback.
Or if you'd prefer to avoid getting into the supporting-a-backup-script business, the Carbon Copy Cloner app is just gonzo flexible.
TL;DR: I'd seriously consider the use CCC here, as backups will have "corner cases"; some errors are to be expected. Errors that can arise here will include full backup devices, offline backup devices, problems with the source files, failures of the cleanup, etc.
