I know that this old house system isn't what you'd use in a RV. I just wanted to bring to light not all MSW inverter are bad. There is lots of photos on the Internet of what is called MSW and it nothing more that a square with a pause as it switches polarity. This I won't even consider a MSW it more a square wave. Yes. I've seen old square wave inverters too.
I will admit the best solution is a true sine wave inverter but quality comes at a price as well. Being I'm also a boondocker and rarely need much for power being where I go there isn't any TV signal, barely any FM radio, absolutely no cell phone or WiFi I can get away with a simple Harbor Freight 1,200w Inverter and solar panel set. Works good for charging a laptop, cell phone, camera batteries, power a CFL Lamp or even my mini-vacuum cleaner. Might fire up a TV once in awhile to watch an old DVD movie but that's rare. No issues.
So my power needs are very low and used low budget inverter and solar but it covers what I'm looking for.
As for air conditioning, microwave, water heater (electric) you will need to consider either twin Honda (or similar) or some sort of large generator. I would not consider doing these devices on a inverter it will just drain the batteries fast. Being weight and storage is a factor I would look at the amount of amp/hours of batteries you got and consider your inverter size and loads against that number. I figured like in my system two 100 Amp/hour batteries (average size) which gives 200 amp hours. At 1,200w inverter will draw roughly 100 amp at full tilt. Giving a max run time of 2 hours tops (theory). But knowing my load requirements is barely 1-2 amps @ 120V at any one time is about 20 amp draw on the batteries that's at least 10 hours of run time (theory).
As for living on 30A @ 120VAC I've been doing it for over 15 years... Love It! 8)