This is a tough one, as someone else has mentioned, it might be a little tough to do it on a budget of $300-$400... The solar panels and batteries could end up more than that. If you're going to end up with a system like that, you might as well just go all out.
This is 4x the cost yes, but as far a prep goes, they can keep food for longer as well. An actual DC refrigerator that is compressor driven and operates on 12V/24V will be more efficient and reliable. In terms of systems it would be more or less the same minimum specs.
200W-230W Solar (single panel) 300Ah 12v battery