As someone previously mentioned, get a deep cycle AGM, (both Optima Yellow & Blue will work, but other brands are fine as well, and cheaper). Main thing is Deep Cycle, 80-100AH. Starting batteries are wrong for this application.
You can get a cheap marine battery box, then add a fused DC outlet + whatever else. Inverter would be optional as most fridges can run on DC.
To add solar, you'll need a solar charge controller and a panel, 100W should be fine. The controller may even fit inside the box, or you can keep it separate. All this should be less than the cost of a Yeti 400, though it might not be as convenient.
With the 100W solar, you may not even have to consider wiring the battery to your rigs alternator/battery, though if you do, you'll need to get a battery isolator, but I don't think that's what you want to do as you were asking about the Yeti.
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