rfuerst911sc, I suggest you consider whether you really want the house to "act like you are in the next room" when the power goes off or if you want to do without some items.
According to
Tons Of Air Conditioning to Kilowatts | Kyle's Converter a 3 ton AC unit uses 10.5 kw of power. With an 11kw generator you don't have a lot of wiggle room for other things. At the very least you should consider a load shedder on the AC. You should do a whole house power assessment and see what you really are using.
We looked at the cost of an adequate generator to run the whole house and decided to downsize. We listed all the things we could do without in an emergency - AC, car charger, outbuildings, pool heater, dish washer, etc and conferred with our Generac dealer. He suggested a transfer switch with a sub panel than only powered the things we really needed in an emergency. The power goes out about 4 times a year out here and we have been happy to get along with partial power.
The box on the left is the main panel. The center box is the old sub panel to the west part of the house. The box on the right is the transfer switch with all the essential circuits when the power goes out.
The old sub panel still powers the AC, car charger, outside pool pumps, outbuildings, etc. as well as the 60 amp transfer switch sub panel (breaker on the lower right). When the power goes out, these circuits all go dead. It still has the old breakers in it, but they are disconnected.
The transfer switch/sub panel powers the refrigerators, freezers, furnaces, water heater,
lighting, and other things we can't do without. When the power goes out, it starts the generator and provides power to all of these circuits.