Many many years ago I built a generator using a 1.6 (IIRC) petrol engine, chosen because it used points and a carb. Biggest problem we found was, at the RPM range we wanted to run it (about 1500), it just didn't have the power. We'd have needed to build a 3krpm screamer to get anything like enough horsepower out of it. The other problem was managing the warm-up, since there was no automatic choke. A very clever chap built a PIC based controller for it, using servos to drive the choke & throttle cables. It worked, after a fashion, but it was always a bear to try to get it stable. It reacted too slowly to changes in load, and the fuel efficiency was in the toilet.
Next attempt used a 1.9 diesel engine, same controller (re-written), with just a throttle control. That worked much better, still a bit sluggish to respond to load changes; the biggest problem was it ate glow plugs, and sooted up something chronic. It was just too much of an engine, in many ways, it was never loaded up properly. Plus it was surprisingly noisy, and exceedingly smoky.
If I were to build another one, I'd use a Chinese horizontal, sized approximately to the gen head, so it ran flat out on full load when everything was drawing power. Cheap car engines sound great in principle, but in practice, they're not really suited to the application, unless you're going with a BIG alternator, and they are surprisingly difficult to dial in.