I've had a fair amount of generic and some job-specific fire fighting training.. so I'll pass on a suggestion or two:
If you can find them the very best fire extinguisher around is a Halon extinguisher.. except for fighting a fire in a high wind, this chemical will bond with the oxygen in the air, making it unavailable to support combustion.. The effective concentration to stop a fire is well below the concentration that can effect your breathing.. not that I'd want to stay in a small room full of Halon anyway, but it is safe.
The neat thing about halon is that it travels.. In an airplane [Halon is the ONLY fire extinguisher on aircraft] there are lots of passageways hidden behind the luggage bins, the window panels etc.. if a fire gets started in a hidden location, you can't find it, and it just grows and becomes more dangerous.. with a Halon extinguisher, we are trained to just make an opening in the panel, or slightly open a luggage door, insert the nozzle of the Halon and pull the handle.. the Halon will travel and bond with the Oxygen everywher it goes and the fire will extinguish..
A CO2 extinguisher , the one that discharges the white fog, needs to displace the air in the room enough that there is very little oxygen remaining, so while these work well in encloses spaces, if the concentration is high enough to be effective on a fire, it is close to causeing the user some 'light headedness' .
A dry chemical extinguisher is like I said earlier, a dry powder blanket, it smothers the fire.. These work well on smooth surfaces like burning liquids. But if you have a fire of logs or rough and irregular objects, the powder can't blanket the sides and bottom of the burning objects, so the fire is just slowed down some..
A bucket of water is very effective on paper and wood, as well as burning seat cushions and carpeting,, the water smothers and cools the fire.
I think last heating season someone started a safety thread, about what was best and needed to have around a stove.