OS 10.13 High Sierra - How do I find a new compatible printer?

AirPrint has been mentioned by a brody and MrHoffman. This driverless technology is compatible with macOS (10.13 High Sierra). A list of supported printers can be found in About AirPrint - Apple Support.

Buying an AirPrint printer is also a good way of ensuring compatibility with even more modern Macs.

Just one thing to watch out for. Even though the AirPrint technology as such will work with macOS 10.13 High Sierra, you may find that the specifications for some AirPrint printer models show higher system requirements. One reason could be that a printer manufacturer provides drivers for USB connections, and/or special software, for example, for setup, ink management, and similar purposes. For example, a printer may have to use an app for setup that does not work with anything lower than macOS 10.14 Mojave. There may be ways around this by using a manual setup, but be especially observant if a supplier offers "free" ink subscriptions, requires special apps, or an always active Internet connection for the printer.

Start here for some ideas and considerations: Which Printer Should I Buy? - Apple Community

AirPrint is present in OS X 10.7 and newer, and will work here. AirPrint gets out of needing vendor printer driver kits, as the drivers are retrieved directly from the printer itself.

Most compatible printers with High Sierra say so right on the box. I recommend going into a Staples or Office Depot and read the fine print on the box. Keep in mind: 10.4< 10.10 < 10.13 < 11.0 < 12.0.

Canon and Brother tend to have better compatibility than other models with older Mac OSes.

Many printers will show up on Airprint, if they are configured to be on the same WiFi network as the Mac. Try to add the printer using the Option key when going to Apple menu -> System Preferences -> Printers and Scanners and see if the printer is detected with airprint if it already has WiFi. HP is pretty good about setting up on WiFi directly from the LCD on the printer itself.