White screen of death after disk full error

My late-2009 Mac mini won't boot after giving a "disk full" error and I keep getting the white screen of death. I've tried booting in safe mode, running the repair disk utility, running fsck -fy, but to no avail. After reading other posts here and elsewhere, I believe my next step is to run target disk mode on another Mac to try and access the hard drive and delete enough files to allow the mini to boot. We have a 2014 MacBook Pro. Does this sound like the best plan and what adapters and cables do we need to connect the mini and Macbook? There are several options in the apple store and I want to purchase the correct ones.