I can't imagine what that's going to sound like when it's running. I camp at Burning Man for a week, and store-bought generators are noisy. I don't even want to know what a generator made from a lawn mower engine is going to sound like.
For your batteries to run AC appliances, you need to know what wattage the appliances draw, then you need to convert the watts to amps:
Amps = Watts/Volts
Watts = Amps x Volts
DC batteries show amp-hours of power, which is to say the maker assures us that the battery will provide so many amps for so many hours. The problem is that if you run a battery totally flat, you wreck the battery, so you have to know what your voltage is pretty much all the time. See
http://www.cieux.com/bm/batteryWreck.htmlfor information on trying to keep your battery from being consumed.
My EEE laptop says its 22W. So if I want to run it off my 100 Amp-hour 12VDC battery, I have 100 Amps x 12 Volts = 1200 watts of power. 1200/22 is about 54 hours, not taking into account inverter lossage.
Or 22 Watts divided by 12 Volts = about 1.83 amps draw -- 100 amp-hours divided by 1.83 amps draw is about 54 hours.
Figuring out what your AC equipment draws is simple if you look at the plates on the back of the equipment. Figuring out what amp-hour battery size you need is simple math. Xantrex, for example, has a FAQ that guides you through the calculations in the hopes you'll buy their batteries:
http://www.xantrex.com/web/id/1040/info.aspI'm sure other manufacturers do, too.
Inverters produce AC from DC in a variety of ways. You need to know if what you power with the inverter _requires_ true sine wave. If so, you need an inverter that puts out true sine wave AC, and those are somewhat more expensive. If your AC equipment doesn't require pure sine wave, you can get square wave or modified sine wave.
If you're pulling lots of power from the battery, you'll need big cables, by the way. I recommend fuses on both positive and negative cables between the battery and the inverter. See here for recommendations on wire size based on draw and length of wire:
http://www.the12volt.com/wiring/recwirsz.aspIf you don't have wire with ample :-> capacity, the current won't reach the fridge and whatever else you're trying to power, and the wire will get hot. The twin concerns are power loss and fire.
I'd suggest lots of research at sites that promote off-grid living, RV and sailing sites, and back-up power sellers (like UPSes).