If you are driving every couple of days, which should recharge your batteries, and you don't run the furnace & standard incandescent lights a lot, you shouldn't have a problem with all of the items you listed except the AC.
The refrigerator of a typical RV will run on propane, using very little 12V power. Lights & furnace are also 12V & will be your largest draw. You would only need a small inverter (300 - 500 watt) to run the TV, however if you want to run the microwave, a much larger one would be necessary along with a larger or multiple batteries.
To run the AC, you need a generator. Depending on the size of the AC, a 2000 watt might work, but a 3000 - 3500 watt is a safer bet. If you don't "plug in" at a campground pedestal or drive often enough to recharge your house batteries, a generator will also be necessary to keep them topped up.
To keep the noise down, look for an inverter generator. They vary the engine speed to match the load & are generally quieter than a less expensive construction type generator. Both the Yamaha & Honda 2000 watt generators are known for their quiet operation & durability, but there are many other less expensive inverter generators.