I tried to solve these concerns with one generator.  I ended up with a Yamaha 2400ishc.  It is a little heavier than the 2k versions, but also a little stronger.  Our has served us wonderfully.  I could move it by myself ( a little tough) and it would run our A/C.  It will run the microwave along with all of the other "small" draw items.
Here's a link to a video I made of ours running the A/C (after installing a hard start capacitor).
Yamaha 2400 ishc running A/CPart 2: FollowupWe just changed over to a motorhome and are currently selling the Yamaha.