After buying a few used phones, I bought a Oneplus One when they came out. (~$400.) While the phone lasted a LONG time and survived many drops, if it broke on one of the falls it would have been a lot of wasted money. Because of how short a phone might last, I'm a big believer of buying used or older phones. Flagship phones from 1-2yrs ago are usually still really good. Might not have the newest and best, but the price/performance is much better than new. And if it breaks it's not as big a loss. Only issue with this method is older phones have the battery already shot so buying a used phone with a non removable battery is a bad idea.
I just picked up an LG G4. I was updating the OS on my Oneplus and somehow bricked it in the process. I needed to get back up quickly so I bought a used LG G4 off of amazon. I bought an unlocked model that was prime so I got the 2 day shipping AND the ability to return it if it was bad. That was $120. 1440 screen, unlocked, IR blaster so I can use it to work my TV/cablebox/etc, Snapdragon 808, 32GBs of internal storage with a removable battery and Micro SD card. For $120 it's a lot of phone. As expected the battery is shot and lasts about 6hrs with moderate use. But a new battery is ~$10 and already on it's way. Finding a used phone off of Amazon or Swappa is the route I'd go. If it has a removable battery just buy a new one off of Amazon. If it's not removable you should make sure it's a newer phone. The newer the better.