The vast majority of computers don't mind MSW (modified sine wave, which is really just glorified square wave AC.). Some audio and video (TV) equipment will produce some hum or whine, or picture artifacts if operated on MSW. No big deal to most folks. Some chargers for battery powered tools don't like MSW (they fry right away). AC electric motors tend to run a bit hotter on MSW, and less efficiently. Your mileage may vary.
You're way ahead of the game on batteries. So called RV/Marine deep cycle batteries are absolutely NOT deep cycle and will die a painful early death in deep cycle applications. The key issue with more sophisticated chargers is that they charge quickly up front, and then taper down as the battery nears full charge. Once charged, the charger just adds enough to replace self discharge in the battery. Cheaper (dumb) charger just reduce to some "safe" low charge rate. It doesn't take into account how big the battery is, or what the temperature is, or how old the battery is.
Good chargers are also generally temperature compensated with a probe on the battery itself. The voltage at which a battery is fully charged is temp. dependant.
Anything you can run directly off your DC source, you will be ahead of the game as far as efficiency goes. Most inverters are only 80% efficient overall. However, it may become too much of a hassle to provide for all those different DC voltages, and there are efficiency losses in DC/DC converters too. You might be ahead to just go with the inverter if the majority of your loads don't match your system voltage (probably 12V nominal.)
Solar panels are pretty much plug and play. Put them in direct sunlight, electrons magically flow. No moving parts. You will need a charge controller to prevent overcharging. Photovoltaic panels are not cheap though. Typically $4.00 per rated watt of output from a good dealer, and "rated" really means under best possible lab circumsances. So if you decide you really need 200 watts of output from your panels, I would buy 400 watts worth, as far as the rating goes.
If you want more (lots more) of an education, there's a free periodical you can download at:
www.homepower.com
They also list lots of vendors that carry all this kind of renewable energy stuff.
This board is also a tremendous resource for home brew stuff in general, and home built wind turbines in particular.
Normally, a build it yourself wind turbine to make electricity will be cheaper per watt of output than the solar photovoltaic panels. Depends on your shop skills, sunlight resources and wind resources. Some do both. If the sun isn't shining, it's often windy. They complement each other.
Sounds like your motor home will be better than new when you're done.
Good luck and have fun!
troy