Keep hourly backups and only keep some of them for each day etc.

backup.sh

#!/bin/bash

# Warning, for each of these rules, we keep the oldest ones
# this is required in order to have some files in the oher category

KEEP_DAY=1 # How many to keep for each day (except for the current 24h and more than a week)
KEEP_WEEK=0 # How many to keep over a week old

for i in {1..6} ; do
        # Find all files that are older than $i days and younger than ($i+1) days and remove them
        find . -mtime $i -mtime -$(($i+1)) | sort | tail -n +$(($KEEP_DAY+1)) | xargs rm -Rf
done

find . -mtime +6 | sort | tail -n +$(($KEEP_WEEK+1)) | xargs rm -Rf