Here in the UK I have installed a number of domestic sized backup generators.
One or two have been whole house units, typicly 20KVA or more.
Most are much smaller. In most homes I would connect all the lighting to the generator, provided that low energy lamps are used, then the installed load is unlikely to exceed 400 watts, and the average consumption would probably be nearer 100 watts for lighting.
With a smallish generator of say 5KVA, that allows effectively unlimited use of all low loading appliances, plus just one large appliance at a time.
For example normal use of lighting, TV, PC, refrigeration, gas central heating,and the like, plus the washing machine OR the kettle, OR the toaster, Or the microwave, but only one such appliance at a time.