Generator selection is a balance of budget, needs and location.
The most popular size of AC unit is 13.5K and it doesn't matter what rig its on, it still takes the same power to run it. It and a microwave at the same time is too much for a 3000w generator.
The least expensive way to run the AC is with a Champion 3500/4000 for around $300. They are long lasting, dependable, easy to start and powerful. The downside is that they weigh 100 lbs and sound like your lawn mower reved up. We use one out in the middle of no where with no neighbors to hear it. When we are in the trailer with the AC going, we can't hear it either.
Next come the inverter generators. These are more expensive, quieter and put out cleaner power.
A 3000w unit here will cost around $2000 new and weigh 150 lbs but they are quieter. The Honda EU3000 is the quietest both at idle and under load.
Next is pairing two of the smaller units together. Two 2000w units combined will provide the power needed. be much less weight individually and if you are not running the AC, you can run just one. With the big brands you will still be spending near $2000.
The prices in the last two options are for Honda and Yamaha inverter generators and admittedly they are the big names here. The only other brand I would suggest right is Champion. There are other second tier manufactures and some have great luck with their products but if they don't, getting parts and support is iffy.
Champion does offer 2000w units that can be paired together that will save hundreds off of each of the units from the big names.
They recently released a 3100w unit that competes with Honda's 3000 Handi. ( a louder version of their EU3000) The Champion 3100 is the same size, weight and noise but instead of $2000 it runs $899.
So if you are camping around others, get the quietest you can afford. Up in the boonies like we are and you can run whatever you want. Personally I hate hearing a generator run and camp at high altitude to avoid the need of AC and use solar for recharging the batteries. This makes my cheap loud generator the quietest of all, the one that doesn't run.