Target Disc Mode from 2009 Mac mini to 2019 iMac I need to transfer some large files from an Early 2009 Mac mini to a 2019 iMac.  The Mac mini has FireWire 800, Ethernet, and USB-1. The iMac has USB-C and USB-3 and Ethernet.

Is this the best way to do it? Is this string of dongles likely to work? Would you risk using Migration Assistant for this, or just transfer the files you need (mostly photos).

FireWire 800 cable --> Apple FireWire 800 to Thunderbolt adaptor --> Apple Thunderbolt to USB-C adaptor
You should be able to connect the two machines directly with an Ethernet cable (if you do not have cabling already) and then enable file sharing on one machine, and locate that machine on the other so it shows up in Finder as a mounted disk.

Then you can just drag and drop the files.