The last thing you want is too install it and find out you have a smokey house cause it didn't draw well. There are too many old chimneys that don't draw well by themselves or need new and expensive flue liners to make them draw.
That said, if you go into the chimney, then think about running b-vent inside all the way too the top unless you use the other chimney for a fire and then an added pipe or the extra stove exhaust may make the other fireplace not draw well. I would hazard to say you may be more happier with the results to avoid the chimney and run new through the roof.
To respond to another question, they make a flange to go over the pipe going through the chimney wall. I think most home cheapos that carry stoves also carry all the necessary vent pipe.
Lets see what the others here say. Good luck and mount it properly and keep the creosote cleaned out so you don't turn the inside wood stove into an outside one after a house fire.