I pondered this same thought and I came to the conclusion that through the ceiling would be better for me. It is also a lot more work to do it this way but I do all of my own work and did not have to pay someone to do it. That being said my chimney (15ft of chimney and 5ft of stove pipe) is a prefab insulated 6" pipe that drafts almost to well. I have my baro set as light as it will go and with a hard fire my baro is fully open and my draft is at -.045 Even when running at a medium fire my baro is open 3/4 of the way and at idle it is still bouncing open (wish I wasn't sending so much warm house air up the chimney). My thought is that you won't have draft issues running the chimney up the side of the house. On the down side of this is the stove pipe will have a horizontal run and require cleaning the ash out of it. If you go straight up the ash will build up and fall back into the stove or be drawn up and out of the chimney. Another thing to consider is the look. Maybe that does not matter to you or your wife but I think a through the roof install looks better than up the side of the house unless it is put inside a chase. But it will cost more to build a chase and actually at that point it may be cheaper to build a block chimney. I got a good deal on my chimney at a garage sale. The pipe is Selkirk super pro and it was never used and I got it for $250 but if I had to buy it new I may have just put up a block chimney. I don't know how long the prefab chimney will last but if you go up the outside of the house and in a few years need to replace the chimney and want to put up a block one, you will have the hole in the wall already and you won't have to patch the ceilings or roof from an old through the roof install.
edit: I just noticed you are getting a wood/coal appliance. If you are burning wood then I would try to keep the chimney as hot as possible to help with the creosote build up and I may be more inclined to go up through the roof. But being that you are having the chimney installed in the winter it may be impractical to go through the roof. I would not want to be working on a roof in the winter and I would not want anyone walking on my shingles in the winter. It would be very hard to install the roof flashing for the through the roof install at this time of year and do a good job of it. If they went up the side of the house they could use scaffolding and not need to get on the roof.