I went through some pain to figure out some USB to Ethernet adapters that work reasonably well on Linux. The pain was primarily derived from needing several dozen of them, not being able to definitively test anything without actually getting my hands on them, and getting bad information from various vendors about how many devices are in stock.
Linksys USB200M – works fine but has a fragile ethernet connector. Uses “ASIX” driver for ax8817x.
Linksys USB300M – also works fine and has a nice short cord to provide strain relief for the connectors. Uses “ASIX” driver for ax88772 (not ax88772a).
Sabrent “USB 2.0 TO Fast Ethernet” (their capitalization), NT-USB20 – seems to work fine, no fragile connectors, but no cord either so one could conceivably damage the usb port on a laptop if the cable gets a yank. Uses “pegasus” driver.