Some also call them SFF (Small Form Factor) PCs but that term for me typically means the slightly larger desktop size PCs you could set a monitor on top of. The 1L PCs are more like the thin clients hospitals have bolted on their monitors.

ServeTheHome has a great ongoing series on "TinyMiniMicro" computers that make great little home servers.

There's a bunch of info about 1L PCs at ServeTheHome. Look for the 'tinyminimicro' tag: https://www.servethehome.com/introducing-project-tinyminimic...

Those guys tend to buy new; although you can easily find used (but still very capable) models on Fleabay, &c. for cheaper. Usual caveats apply; but I've had good experiences after checking sellers carefully.

Manufacturers also have factory-refurbished sales websites, usually separate from their normal website (lease-returns from their financial services arm). Those come with short warranties, and an option to extend them. They are also nicely cleaned up and re-boxed, sometimes with accessories.

I have one from Fleabay and another from Dellrefurbished. Both have been running great for nearly 3 years.