I tackled this from a different "angle". I installed a sub panel many years ago to add circuits to house and shack. I have moved important circuits to it and transfer sub panel. Granted I do not have full house power but then I do have a more balanced load for generator. Main panels are usually 100 amp or more (mine is 200). With a 200 amp main they do not have to be very fussy about load balancing in a house and it is easy to have one 120 volt leg overloaded long before you reach two leg capacity of a generator. A 5k generator is basically a two 22 amp 120 volt feeds which is peanut on a 200 amp panel. If you do a whole house transfer realistically you should use a 10k or bigger for 40+amp support for each 120 volt leg. For what its worth....
Good points. Most folks don't want to size an emergency generator to supply their whole house load. Probably would amount to a 25KW machine, assuming whole house HVAC is tacked on. The fuel to run the puppy at LPG prices wouldn't be cheap, even for a few hours. So, move critical branch circuits to the sub panel and only transfer it to the generator.
A 60 Amp sub panel is about the smallest one can get for a low price. The other cost factor is the transfer switch. Not cheap. As for the motor-starting problem with the furnace blower, the size of the generator has to be large enough to supply the starting inrush and not slow down. Just a guess, but if it's a 3/4HP blower motor, the inrush would be almost 16A at 120V assuming a 300% inrush.
Last time I looked, a 200A transfer switch was about $300 or so. And, that's for a manual switch. A 60A one would be much more affordable.