As the subject of this thread mention "Lightroom Backup" folder but you didn't include a screen shot of the that folder. If indeed you're interested in what to keep in the "Backups" folder, the answer depends on how risk tolerant you are?
If you're a 'nothing bad ever happens to me, throw caution to the wind" type of person, you only need to keep the lates few zip files in the backups folder
If you are the type of person who always gets the maximum amount of insurance and never invests in anything at all risky or volitile, the keep them all.
But, if you are a more middle of the ground person, establish a plan that has you keep more of the most recent backups and fewer of the older ones. Let's say you take one back up each day you actually change anyting in lightroom, a middle of the road, but a bit on the conservative side would be something like this:
- last 3 months - Keep them all
- The year prior to that - keep first one of each month
- The next older 5 years worth - Keep first one of each quarter
- anything older than that, either delete or keep the first one of each year.
Of course you can adjust up or down if you think this is too many or too few. Or, if you have tons of disk space, just keep them all and don't worry about it - they don't affect performance disk space is short.
DON'T FORGET THAT THE BACKUPS IN THE LIGHTROOM BACKUP FOLDER IS JUST THE CATALOG - NOT THE IMAGES. BE SURE TO BACK UP YOUR IMAGES AT LEAST AS OFTEN AS YOU BACK UP YOUR CATALOG OR ANY OTHER ITEMS ON YOUR COMPUTER YOU CARE ABOUT.
One other thing, There is a "Backups" folder in your screen shot which may or may not be the folder currently iused by LrC when it exits. As this folder is in the same folder as your catalog that is better than nothing but not much. It will protect agains Catalog Corruption, but not a disk drive failure, theft of your computer, or a natural disaster such as fire, flood, tornado, hurricane, etc. You should be backing up to am external drive connected to your computer AND to some cloud service or other offsite storage.