Remember, it's best to keep generator load at 75% of max, full load only for short intervals, if you want to lengthen the lifespan of the generator, not so much for the motor, but for the electronics to keep them cool. So while a 2kw might seem like enough just going by the spec sheet, realistically it shouldn't be used to output more than 1500w at any one time.
So my suggestion is to audit your expected power consumption, add 25%, then find a Genny that has at minimum whatever number that came too, or the closest size above when rounding up.
And there are kits out there to convert a non remote start Genny to having a key fob and remote start. I've seen them for the predator gens from harbor freight.
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