There are many small very cheap 2 cycle portable generators that you can buy. They are sold under several makes and models:
Chicago Electric 66619 from Harbor Freight 800 to 900 watt
And many many more.
Many of these have one thing in common, they are cheap crap/utter turds. They all look pretty much like this:
But these turds can be polished.
If you buy one of the above generators (or one like them), before you start it up I recommend the following:
Replace the spark plug with an Autolite 65, or 64, or an equivalent type spark plug.
Gap the spark plug to between .028 and .031.
Torque the spark plug to 25 foot pounds or 360 inch pounds. The spark plug that comes with them are often cheap junk and not gapped correctly.
Remove the gas tank.
locate every connector that looks like these:
Inspect the fuel line, if it looks like smooth plastic and possibly has a mold seam, replace it with real fuel line. I would recommend replacing it anyways. Many of these use a plastic fuel line that will swell, split, or deteriorate in a very short time.
replace the fuel line hose clamps with good ones.
remove the fuel valve and replace the gasket pointed to in the picture below with a gasket or washer that holds up to gasoline. The washer installed is plastic and will not last long.
Put gas in the tank, wait about 5 minutes for the carburator bowl to fill, and start the engine, with the choke full on, move the choke over to run, and connect a 200 watt load to the generator wait 5 minutes. Using a volt meter check the voltage (under load) it should be 120 volts AC if not adjust the screw in the recess shown in the picture below (the red arrow). If the engine sputters when doing this adjust it as close as you can to 120 volts AC and the engine still runs smooth. let it run for several minutes and monitor the voltage, adjust again if necessary.
Drain the gasoline if the generator will go unused for more than a couple of months. You will have to remove the gas tank and fuel valve to do this. If you do not, the gasoline can turn in to varnish and clog the fuel valve, line, and carburetor. Leave the fuel valve open while it is being stored and the gas cap loose to allow the remaining gasoline to evaporate.