... nor to run your 1500 watt cook-top. If you're thinking of doing any serious AC-powered work you should consider a Honda EU2000 or Yamaha EF2000is. Those are impressively quiet (especially when running at slower speed in "eco mode") and will set you back about a boat buck, but heavy battery draw is a slippery slope... It means a bigger bank, a powerful inverter, and more robust charging capability -- all of that will cost (and weigh) far more than the above-mentioned inverter-generators.

If you're not thinking in terms of using at anchorages, you might choose a lower-priced Chinese-made knock-off inverter generator (eg Kipor, Honeywell, etc.) -- but they will be at least twice as noisy, and less reliable. Subaru Robin also makes one but in that price I'd go for the Honda or Yamaha.