We're going through the same thing right now and I have 2 proposals in front of me. Both places install Kohler and Generac and both suggested Generac. Our house is about the size of yours but we don't have a hot tub, which I don't know if it changes the electrical load enough to get a bigger generator, and they suggested 18kW. I'm assuming you have central A/C as we do also. Price to install is about $8,500.
Unfortunately we don't have gas or propane here so I have to get a separate quote to install propane tanks but since you have gas to your house you don't have to deal with that. I don't know if we had gas whether there would be an additional cost above the $8,500 to hook up the gas to the generator. Probably minimal cost anyway.
$5,000 to $6,000 seems low but maybe Chicago is cheaper than Boston. Of course you probably know that the cost for generators has gone up the last year because so many people are getting them. Lead time to get the generator could be 6 weeks they said since they're flying off the shelves (if you could fit one on a shelf!).