Owner of a wood-burning stove here. The Ded residence has hot water underfloor heating, with a gas boiler. That keeps the house (which is very well insulated anyway, after the renovation) comfortably warm, and the stove is a tad oversized for the room, but it adds some extra warmth on colder days. Essentially, it is far more cheerful to be able to see leaping flames. Oh, and the cats like it ,too, they like to lie in front of it.
Some asked if gas fires are safer these days. Gas stoves at least have a flow cutout device if they are turned on but there is no flame. Gas fires probably have the same by now, given that I have not bought on for three decades. The good points are that they are easy to use.
Pellets? I have only heard of them being used for boilers, not in fireplace stoves. They cost more than firewood, and you need a lot of storage space. Otherwise, I have no experience with them.
Cost? YMMV. It depends on the cost of firewood and gas in your area. Wood is cheap where I live, gas is is somewhere in the middle, and electricity is very expensive. The stove also gets the bigger bits after various trees are pruned.
Pollution? A good modern wood stove fired with dry wood produces very little pollution or smoke. Avoid using resinous wood such as pine, as it will produce a lot of smoke and soot. If I find pine in a batch of new logs I just thrown into another pile and burn them up in the barbecue or in the burn bin to get rid of garden rubbish. My (British) stove is exceptionally clean and does not even have a catalyst. Dunno if they ship to the USA, but I was not on their regular shipping routes either.
Hard work? Firewood warms you twice over, the first time being when you split it. But you get a free workout. It takes a while, too, it took me two weeks of intermittent work to split a truckload of wood - and it was a small truck. You have to stack and dry the wood, and carry it to the stove, light the fire and clear out the ashes. It’s not really a big deal as far as I am concerned, but YMMV.
So; a wood fire is more fun but more work. I took a vote on it - and got outvoted by the cats, so a wood stove it is.