When looking for a generator you must also check if the nameplate rates the output as continuous. I have seen generators rated at 5kw but only 3200 watts continuous. That 5 kw generator probably can handle start currents for small motors but 5kw of continuous load would overheat it.
Also be aware that a lot of small generators are air cooled and the heat they make at full load is enough to start a fire if cooling air is deficient.
A lot of generators are not designed for use as standby for a house but only for portable use and their grounding scheme could violate a few codes when connected to your house
