Disk storage low. What can I get rid of

This may help.Optimize storage space on your Mac - Apple SupportIf you are using Time Machine< you may want to delete the snapshots stored on your computer.https://eshop.macsales.com/blog/77372-how-to-delete-time-machine-local-snapshots/

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

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How to delete Time Machine snapshots on your Mac

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The final word from Apple on Managing the " Other " Category

Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

The only files, as you say, buried in the OS, would be the snapshot files that “my ginger” referenced. However, normally the largest collection of files would be due to stored videos/movies, music, photos, and mail attachments.

You could start up in safe node, which is slow. But it will clean cache files.https://www.macworld.co.uk/how-to/how-use-mac-safe-mode-3623521/ Some system log file can be deleted, but that is not big gain in space. Anything deleted in you library system folder could cause problems as most of it is part of your operating system. If you have deleted third party apps or programs by deleting just the main app or program will leave other files spread thru your operating system. Always look for an uninstaller in the app or look up the best way to fully uninstall. Omnidisksweeper can help find files. but be careful how you use it.https://www.omnigroup.com/more

Move user created content only, original or copied, to free up space. Never delete any system type files and folders.

You can move the data to an external drive or a cloud storage service; iCloud is not designed for long term autonomous storage

If I read between the lines - think the computer may have the tiny 128 GB Internal SSD ?

If that be the case - IMHO this size SSD should have never been made available at time of Purchase.

No matter how clean the operating system is - it will be very difficult to keep the suggested 15 % to 20 % of the Total Drive Capacity as Empty Space for normal and good operations.

This will be compounded by the possible upgrades from several earlier versions of macOS to current version Mojave .

Possible workaround, but do not attempt if not certain one what's the newest Qualifying version of macOS for this computer.

It would involve a Scratch Earth approach and even after that, the 15% to 20% Empty Space is going be a challenge