I've been spending a lot of time researching the same questions. Planning on adding some solar to the Roo this spring.
On the inverter, I agree - its about as clear as mud whether you absolutely need pure sine or not. Sounds like the microwave isn't going to like modified sine wave, but I can't see running the microwave on battery, so I scratched that as a concern. Flourescent lights and variable speed motors seemed like no-no's for modified sine wave, but I don't have any of those in the camper. I read some chargers and adapters don't like it either. However, I have a cheap 400W Diehard modified sine wave inverter that we used for several trips to power the laptop and cel phone charger while driving on long trips. I guess ignorance was bliss - everything worked fine. Never even thought about it until I got into this solar project. It was a plug so we plugged them in and everything worked...
So, I just scored a good deal on a Xantrex XM 1800 inverter on e-bay. My conclusion after a lot of reading was that I wanted a hard wired inverter with a transfer switch. This fit the bill at a reasonable price. With the camper covered for the winter, and now burried in snow, I haven't had a chance to try it out yet.
There seem to be a couple common setups out there:
Basic inverter with only recepticle output for 110V. Then you plug in what you need directly, you make up a double end cord and backfeed one of your circuits, or you add a couple 110v outlets and connect them with a plug to the inverter. If you want pure sine at a fairly low cost, this might be the way to go. May or may not get any remote panel in this setup.
Option 2 is what I did. Something like 1000 to 1800 watt inverter with hard wired connection points and a transfer switch. Then you can add a sub-panel and power a couple of circuits. The beauty of this is when you have shore power, everything works as normal and it will automatically switch to battery power when not connected to shore power. These middle of the range inverters either come with or have the option to add a remote panel, which I think you really need in this setup. Gives you the on/off switch to save battery when you don't need the inverter idiling and gives you a current reading to monitor battery charge. I plan to wire this in a slight variation by just running the camper's one 110V circut through the inverter and back to the breaker panel. Works the same as a sub-panel, but you don't actually have to put in second panel - just wire the inverter in between the shore power and the exisitng breaker.
Then option 3 is the high end system. Big 2,000 - 3,000 watt inverter/charger. Has a good 3-stage charger built in and you disconnect the cheaper factory supplied charger. Takes better care of your batteries when on shore power. Then the inverter is hard wired and you use the subpanel to run multiple 110V circutis. In large MH's and TT's where you have big loads, this is the way to go for extended time on battery power. Then you go with 4 or more batteries. This is pricey. The inverter/chargers start in the $1,000 range ang go up from there. If you plan to add solar, your solar charge controller is probably going to be a 3-stage controller. Get a decent one and if you store your camper in the sun, let the solar maintain your batteries, which gives you a good quality charger without the extra cost of the inverter/charger.
Here is a link to a comparison chart on the Xantrex models to compare some options:
Power Inverters Comparison Chart
Hopefully this winter weather ends at some point so I can get this stuff installed. This got rather lengthy, but hopefully its helpful...