Agree with the others, look into bottles as balcony/ deck is not ideal for a generator. But, since your question was about generators, that unit says it needs 585 watts. Your post said 2 units. If you're running two, you need a bare minimum of 1170 watts. Like others suggested, add 30% (ish) for surge and you're looking at about 1,500 watts. If you're only running one unit at a time, then 750.

That's low enough, you could also look at getting a car inverter. I just checked on Amazon and found this one. inverter

A lot easier to store, you don't need fuel for it, and no toxic fumes (other than the car obviously). It's also a lot cheaper.

The magic words you're looking for when generator shopping are "pure sine". That means it's "clean" power in that it plays well with delicate electronics.