A chest freezer is used for fridge0 for the same reason that freezer conversions are often used for offgrid fridges: Efficiency. Not dumping cold on the floor when the door is opened is the usual explanation.
There are many articles on the web about chest freezer conversions, how to organize groceries for easy access, etc.
Any standard AC powered chest freezer can be used for fridge0. It could even be a used freezer, but that could be less efficient.
Bear in mind that the added thermal mass used by fridge0 will reduce the storage space.
location
It's a good idea to put the fridge outside or in an unheated building to reduce power usage in the winter. But check if the manufacturer says it's safe to do this. Some manufacturers do not warrantee chest freezers used in a below freezing environment, for reasons that are unclear.
Joey Hess's fridge0
I bought a new Frigidare model #FFFC09M1RW, 8.7 cubic feet interior size.
It's rated to consume 138 watts (1.2A at 115V). I measured it to use 120 watts.
It's been working for me very well. I keep it on the porch, which is not ideal in summer, but there's plenty of power then, and has proven to be a good idea in winter since it often doesn't need to run at all then.
One initially surprising thing is that if the fridge is running when power is disconnected and then reconnected, the fridge won't immediately start back up. Seems that it detects the motor/compressor is too warm, and they need to cool down. This doesn't cause any problems in the fridge0 build, though.
others
Please add your chest freezer information here if you do a fridge0 build.