I have a wood stove in the lower level of my bi-level and of course it gets a lot hotter downstairs than up so I turn the furnace fan on occasionally to even out the house. I also installed an exhaust vent in the ceiling downstairs (almost directly above the stove) and ran a 4" duct up through the cold air return and into the upstairs living room. The 4" vent is right behind the face plate of the cold air return. You can't see it but you can feel the warm air blowing through it.
I also like to run the furnace fan because it helps clean the air in the house. We have 2 dogs, a cat and a bird that just love to clutter the house with dust and dander. Not to mention wood stoves can be a little dirty!
As long as there is no propane running thru the furnace I'm happy.
Electric bill? I don't run the furnace fan enough to even notice the difference. The blower for the wood stove is connected to a snap disc thermostat and comes on and off as stove temps dictate. The vent in the ceiling is on for 8 hours a day. The Christmas Lights are on all night, the chicken/duck coop custom water heater is on 24/7 and their light is on all day long. Momma and the kids usually leave at least half the lights on when they leave the house in the morning! LOL
Last year I was running a fireplace not a wood stove and had to use the furnace at least twice a day and it would kick on at night as well. We also supplemented with an electric radiator style heater.
November bill last year vs this year....$65 difference. Also the gas valve on the furnace is off!
I have 2 rooms in the house that are not used for anything but a guest bedroom and one is empty except for a cat litter pan. I keep those doors shut (swinging cut out door for cat) and also close the vent/cold air returns.
No sense heating rooms for nothing!