I have a 2000 sq ft house, with air conditioning, swimming pool circulation equipment and normal lighting, ceiling fans etc. The breaker panel is rated at 200 AMPS. I want to have a standby back-up electrical generator that will have enough power to run the A/C, pool, range, and normal lighting, TV, etc. I am planning to power the generator with Natural Gas. How large should the generator output be?

Figure out how many watts of power your stuff uses, many times you can find this out by looking at your monthly electric bill. Starting an appliance motor takes usually twice the electricity as actually running it does(--think about starting your lawn mower, you have to give the pull cord a good jank to get it started, then after it starts it keeps running by itself.)
So figure in some extra wattage for that reason.

Not a bad answer. For motors look for a unit of VA or volt-amps. It does get a little complicated, but for starters you need the watts or VA rating and voltages for all the stuff that you need running at the same time.
Watts and VA are basically the same unit, but 746 Watts/hoursepower does not include the amount of power to start the load.

Some tricks can be done by your electrical contractor such that the pool and AC can't start at the same time if needed. Backing up the AC and range is going to cost you big bucks.

Then there is questions on moving these loads to a sub-panel or having manual or automatic transfer whena power fail occurs.

I would say you need 15Kw at minimum, and that is NOT including the range.

FORGET about including the range. WHY would you possibly need it for the rare and short times the power is out??
For the added $$$$$ it is going to cost to be able to run the range you could buy a LOT of hot plates and Coleman stoves.