Though a 2,000 will not run the A/C.. it will the microwave, a 1,000 will not.
And if you get a Honda EU-2000i-companion, and a low cost parallel kit, or two E-2000i and a high cost parallel kit,, it WILL run most Air Conditioners.
Same is true of all the makes with a parallel kit. Though only the Honda makes a Companion model far as I know.
I would not mind a Genrac 1000 (Traditional generator) one serial number in particular, or a Yahama EF-1200i.