I use regular 87 octane E10 gasoline without any problems. I add 1oz of TCW-3 marine 2-cycle oil per 5 gallon gas can. I also put the blue Stabil 360 in the gas can (amount according to the label on the bottle). Both these go in right at the gas station when I fill the can. Never a problem with gas anymore.
When you are done using the generator, drain the tank, run the engine out of gas, then drain the last drops out of the carburetor (if possible). At this point you are good to go. Any remaining gas in the tank and carburetor will eventually evaporate and leave a slight oil film that prevents corrosion. Also, pull the starter cord lightly until you feel resistance. This indicates the engine is on the compression stroke and both intake and exhaust valves are closed (which protects the piston and cylinder from outside air and condensation/corrosion). Next time you need the generator, put gas in it and start it up!
As for break in, while running, vary the load on the generator (alternating between nothing, to 25%, to 75%). Then before you shut it down, let it run unloaded for at least 5 minutes for it to cool down. I usually run it for 20-30 mins the first time, then change the oil. Then run it again for an hour or two, then change the oil. Use a clean oil drain pan and check after each oil change for metal 'glitter/sparkles' in the oil. This is common for break in of a new engine. If there is still glitter in the oil pan, change it again after 5 hours. Repeat until the oil drains clean. My lawnmower and generators drained clean after 3 - 4 oil changes. Then, change oil according to the manual (usually every 50 or 100 hour intervals).
Use whatever oil in the proper grade that you want. It is only in the engine for a short time. no sense using the expensive stuff for break in. I had a bottle of conventional 10W-30 oil that I used for break in. When that was used up, I switched to Mobil 1.