I guess I should be a little more thorough.
1. Out of all the criteria, official LineageOS support is the easiest list of phones to start off my search. It is just a matter of going to the website and looking at the list of supported devices. I know hope that the supported devices will get consistent OS upgrades so they won't have to worry about their phone getting outdated because the manufacturer or carrier is too cheap or lazy to push updates. It just recently happened to one of my family members and I would like to prevent it in the future.
2. I weed out all the deal-breaking phones, it varies person to person. For me, I wanted a phone with USB type-c, top of the line SOC, local LTE support. I ended up picking an Axon 7. For the prior-mentioned relative, it needed to be less than $50. I recommended a used Nexus 4, Moto G, or Galexy s3.