The K1, K2, DX and DXG are best avoided because Download & Transfer will only be mobi, which is very limited.
The later old ones may need updated for azw3.
See
https://www.amazon.com/gp/help/custo...MQC26VQQMM8XSW
A registered updated (3.4.3) and synced at least once since K3 /Keyboard 3 model does allow azw3 on "Download and Transfer". Originally it didn't do azw3/KF8.
The azw3/KF8 is similar to epub2. The Mobi format was obsolete even before the first Kindle in 2007.
You might need to replace a battery to get an old kindle to go long enough to update/register.
Also registration for older Kindles needs you to give your Amazon account a phone number for SMS and then you get a code. Though email may be possible.
The Kindle itself isn't used. You register it, copy & paste the serial ID off your Amazon web account into the deDRM plugin. Then the Kindle can live in a drawer for ever. You download ebooks from Content & Devices on your Amazon web account on a Mac/Windows/Linux (though iOS and Android browsers can work, but you need then to copy the file to the Mac/Windows/Linux computer running Calibre).