You need a power curve for the engine to determine what size generator end to install. A 4 pole gen runs at 1800 RPM , 2 pole 3600 RPM. Small backup generators usually run at 3600 because a smaller engine can be used than a gen running at 1800. Some installed home backup generators use belt drive so the engine runs at ~ 2400 RPM to split the difference between low engine RPM / engine size.

I tend to like the engine a but undersized for the gen end, this way if you overload the system it will drag the engine down rather than burning the gen end down.

What are you going to use the generator for?

If you are going to run a house, a construction site light tower could be a good choice. These usually have small 3 cylinder engines coupled to a 6 to 8 KW gen end.