Your inverter, batteries, and solar panels only have an indirect relation when it comes to capacity and the inverter has nothing to do with the solar panels. And you're missing the charge controller that goes between the solar panels and the batteries.
Sunlight goes into the solar panels which, are connected to the controller. The controller manages the amount of energy being passed to the batteries for storage. The inverter lets you draw stored energy from the batteries for 110V AC devices. The greater the capacity of your solar panels, the faster they'll charge the batteries but only up to the capacity of those batteries.
So the first thing you need to determine is how much power you need to have available between charges and the maximum amount you will need to draw at any given time. That will determine the correct capacity for the other parts of your system. You need an inverter that can handle the maximum load (Microwave + TV + lights + whatever else you'll be using simultaneously). You'll need a battery bank that can store the total amount of power you'll need. You'll need to have solar panels sufficient to collect enough energy during daylight hours to fill those batteries and a controller that can handle the current.
Honestly, your best bet is going to be to consult with a local solar installer. Any installer worth his salt is used to helping people figure out what their power needs are and can help them design a system (and adjust their usage habits) so you end up with the correct match of collection/charging/storage/inverter. As far as determining the correct numbers, an RV is the same as an off-the-grid cabin, even down to the generator for backup power. Even if they don't have RV-specific experience, they can still do the design work and you can adapt that design to the RV application. Just make sure you're clear up front about whether you only want design or if you're hiring them to do the entire job and find out what they'll charge for their work.
I've got a 4800 watt grid-tie solar system on my house and, with over 2 years of data at my fingertips, I can definitely confirm jauguston's comment about variable power output. Those cloudy days will kill you. That's when you have to kick on the generator. A rainy day can cost me over 20 kWh in the summer. June 3, 2011 was 29 KWh. June 4, 2011 was 6 hWh. Time of year also makes a big difference. I average high 20s in the summer and low 10s in the winter. Trees will also cut your production considerably and, unfortunately, the days with the best solar energy production are precisely the days you want to be parked in the shade. Otherwise, you're dumping all your energy into AC and you'll be losing ground.
My system, installed 12 years ago, was calculated to be a balanced installation. I have 3 120 watt panels, 4 12 volt glass mat batteries, and a 2500 watt ProSine inverter. My controller is a Solar Boost 2000. The solar controller and the inverter/charger have temperature probes on the battery bank -- very important. The ProSine has a 100 amp multi-stage battery charger providing the capability to restore the battery bank quickly from the generator or shore power. The solar controller and the inverter/charger are the brains of the system. Don't try to save money on them.
Can't remember the technical detail, but there is something important about the voltage of the panels. Got to produce 14.7 or so volts to drive the batteries to full charge. Seems like it was something about groupings of 7 instead of 6 solar cells on the panels.
Greatest thing about solar. My MH sit in storage for 6 months - when I retrieve it the battery bank reads 14.0 volts.
Unfortunately health is forcing us to a small class C to continue the RV lifestyle.Sure gonna miss that solar!
"A beach house isn't just real estate. It's a state of mind." Pole Sitter in Douglas Adams MOSTLY HARMLESS
BTW, I would look at that inverter power consumption while in standby. Some of those inverters can draw quite a bit of power doing nothing. As far as inverter for your fridge, that would draw alot of current and you may need alot more solar and batteries if you are going to run a regualer fridge.