volts x amps = watts
so read how many amps your smoker pulls, its on a label on the smoker itself somewhere near the plug I would imagine
so 10 amps times 120 volts = 1200 watts and thats what your generator is sized in.
I would try and size mine about 80% of the rated load.
If you really want quiet I would suggest one of the RV inverter generators such as honda, yamaha, or similar....costly but much nicer on the ears, and after listening to a motor run for 12 hours, you may appreciate quiet.