I've got a question that I've tried to find out on my own, but with questionable results. Can you use kitchen appliances that are meant for a stationary home in a skoolie that's setup for boondocking?
Brief answer is "Yes".
Generally you will want smaller appliances. You are fitting out a "Tiny house" not a McMansion.
Fridge: The biggie, because of the power requirements. Modern domestic fridges are super-efficient and demand much less power than the usual "RV" fridge that runs on 12/120V. It's because they work in a completely different way. Try a Magic Chef od around 10 cu foot capacity and run it from your inverter. Power consumption is very modest, but still large compared with most electrical you use. RV makers are now, by and large, fitting domestic fridges in their units. There are some marine fridges that are very efficient, but they also cost a fortune. There is little to be gained by fitting a chest-style fridge either.
Microwave .... You will want a lower powered mw. Even then it will require a decently large inverter and battery bank to run, or a small generator.
Stove ... I'd go for a smaller domestic stove, or cooktop and oven, that can run on propane out of the box. I plan on using propane for cooking and water heating, and for a barbeque with an external propane skin fitting. That is, you plug the BBQ into the bus to use it.
Those are the major appliances. There are other ways to do this, but broadly that's what I am looking at doing.
Bear size in mind. You have to get them into the bus.