I am in need of a new burner phone and hoping I can get some recommendations on here.  I would like a phone that is ideally per-loaded with minutes and does not require a credit card to purchase.  I appreciate any feedback!

highly doubt you'll find those anymore.

have a flip fone buy 60 minute card for $19.99. usually get bonus minutes or 2x or 3x, only need to renew every 3 months. cheap about $20.00 sometimes less than that on sale. the bad news on 1-1-2021 almost all tracfones will need to upgraded to a new system, so you have to buy a new phone.

WHICH ones? Tracfone contracts with various major companies. Does this have anything to do with CDMA, TDMA, and GSM?  If I have a GSM Tracfone will I be OK? ... I guess I should just look it up. But thanks for the alert!

TracFone is offering several.  LG Rebel 4 (Android 8), for instance.  
For lowest cost use their $20 90-day refill cards (not "Smartphone" cards).  
I keep accumulating unused minutes/texts/data due to light, hobby-only usage.  
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Sometimes Amazon offers TracFone pre-loaded bundles that could be what you seek.

Is there a used model you recommend?  I can buy on Craigslist.

No, not "almost all tracfones".  
The ones that need to be replaced are older models that do not support VoLTE (4G) and are on Verizon CDMA network.  
(TracFone does not have its own network/towers, but leases from other companies.)
Any TracFone you get now (from them) will not face this problem.  OP is safe.  
I had a flip phone as my first hobby phone, and found it pretty unbearable for my main use, texting.  Cheap "smartphone" has been the right thing for me since.  

Just go to Walmart. They have a ton of “burner phones” there.