Minimum of 3K watts needed for reliable genny operation under most conditions. Yamaha, Honda, and Champion all have inverter generators that could be paired if you go the 2K watt route, and they have single 3K units if you prefer purchasing one generator to do the job. Good customer service has been reported for the brands mentioned above.
The Champion 3K unit is a popular choice and remote start is available if you want that option. Why pay more for red or blue when the generator is something that gets little use in the scheme of things. We have solar to charge our pair of 6Vdc GC batteries, but having a generator that can power our entire rig makes for trouble-free camping under any conditions.