There are a variety of generators available but first answer these two important questions:
What do you need a generator to power?
What type of fuel is available for the generator?
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Generators:

Noise Level - Anywhere from "nuisance" to "How anything could be that loud"
Cost of Power - The least expensive cost-per-watt backup power available
Power Quality - More expensive models tend to produce "cleaner" electricity that is better for sensitive electronics
Fuel - Models run on gasoline, propane, natural gas, diesel or multiple fuels
Carbon Monoxide Alert - Generators produce carbon monoxide and must be operated in a well ventilated environment
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There are also a variety of inverters available but the same questions apply:
What do you need an inverter to run?
What power sources do you have to run an inverter?
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Inverters:

Noise Level - Nearly silent with only a cooling fan producing sound
Cost of Power - More expensive cost-per-watt than generator backup power
Power Quality -"Pure" sine wave inverters mimic grid power while cheaper models produce a square wave power
Fuel - Battery, solar or connect to an automotive battery for backup power
Carbon Monoxide Alert - Inverters themselves do not produce carbon monoxide though it is a consideration if you connect one to your car or truck


The latest trend in portable power generation and the same questions apply:
What do you need an inverter generator to run?
What type of fuel is available for the inverter generator?
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Inverter Generators:

Noise Level - Engineered for quiet operation
Cost of Power - Higher cost-per-watt than inverter
Power Quality - More expensive models tend to produce "cleaner" electricity that is better for sensitive electronics
Fuel - Most commonly run on gasoline
Carbon Monoxide Alert - Generators produce carbon monoxide and must be operated in a well ventilated environment
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Expensive with declining costs every year:
What do you need solar to run?
Can you convert the power to something usable?
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Solar:

Noise Level - Nearly silent with only a cooling fan producing sound
Cost of Power - Still the highest cost-per-watt power available
Power Quality -Depends on your inverter and battery bank - No Sun=No power
Fuel - Think of the upfront cost of solar as buying all your fuel at once
Carbon Monoxide - Not in a solar house