If you choose the fire extinguisher route, and there's no problem with that (just be aware that in homes that have even small fires it gets very smokey real fast) choose a suitable mounting location, I've gone to some many homes and seen fire extinguishers tucked near by the most likely source that would cause a fire, thats no good, you should have the extinguisher near an exit door, that way if you ever have to use it, by the time you grab it you can make the decision to leave the structure to safety which in my opinion is much better then trying to stay and fight a fire.
Also if you have a chimney fire, the chimney can reach temps of 2100 deg f, if the chimney is on fire, the choice extinguisher is an abc powder, either shoot it up the baffle of the stove, or open a clean out if you have one and shoot it up, the draft from the chimney burning will suck the powder up and either buy time for the fd to get there or extinguish the chimney fire.
That. I even saw a pic on here with the extinghuisher on a ledge above the stove...
Near the door: either upon entry you can get it and use it, or at least fire won't be between you and the exit without access to an extinguisher. Imagine having an extinguisher, but you have (christmas tree...) fire, and the extinguisher is on the other side....