I'm sure someone with more electrical knowledge than me will chime in; but my understanding is that if you want to run an air conditioner while going down the road (not to mention the fridge), you will need a generator. Either that, or a bank of batteries so large and expensive as to be unreasonable. I think the 110v AC unit alone pulls too much power to be run off your alternator via an inverter. If you want to run any lower demand 110v items (like the TV) on the road without running the generator, then you need 6v or 12v deep cycle batteries hooked up to an inverter big enough to handle your anticipated demand. For plugging in to campgrounds I think you need a separate 110v electrical circuit. There are also converter devices to transform AC to DC power (110v to 12v).
My plan is to keep it as simple as possible. I will have an inverter and a couple batteries so I can run either DC or (low demand) AC items when on the road, but when I plug in at a campground I will generally run only my AC circuit. If I want to run air conditioning on the road I will get a generator. I do not plan to have an electric fridge. I figure for my usage, a cooler is fine. I don't like the idea of a fridge causing constant energy demand. You can turn the air conditioner off, but a fridge must run or your food goes bad, and beer gets warm (horrors!)