I third the notion to buy only from Apple. eBay, Facebook Marketplace and other such sources are a hotbed of stolen or lost phones (mostly stolen). You end up with a phone that arrives activation locked and the seller disappears with your money.
As explained by lobsterghost1 and sberman, Amazon Renewed only means someone there looked over a used phone to make sure you can set it up as new, and maybe cleaned up dirt and light scratches. It will otherwise look the way they got it.
The only third party site I would even begin to recommend would be gazelle.com. They buy and sell used devices. But, they sort items they have on hand by Fair, Good and Excellent, with the price increasing by rating. There are problems even with excellent. One is, they guarantee you'll get a charger for a phone that originally came with one. Except, that doesn't mean it will be a genuine Apple charger. There's also no telling how old the battery is, or what its condition is. You get what you get.
We once bought an iPhone 5 there marked as excellent. Um, not impressed. Overall, the phone looked nice, except most of the central area of the screen was pink from being swiped thousands of times. That is not excellent condition. And once you get up into Gazelle's Excellent pricing, you may as go to Apple's refurb page, where you will get a far superior device for pretty much the same cost.