You are the beginning of a fun learning curve! Enjoy it!
Yes, a residential refrigerator will work just fine. I have been doing it for several years, many RV's have been doing it far longer. The key is having the electrical system to support it.
There is no such thing as a "solar bank" - you will most likely have a battery bank that has multiple charging sources (shore power, generator, solar array). To power 120VAC accessories in your rig, you will need an inverter that produces 120VAC from whatever battery bank you have (probably a 12V bank but other is possible). Of course, this can result in significant power consumption from your battery bank and it needs to be sized appropriately. Solar charging is a magical thing but when done well, the system is designed to match your needs.
In the context of refrigerator, you mentioned propane. This is typically a two-way absorption refrigerator commonly used in RV's. They work but are expensive and the venting at the back can be difficult to get right.