Woodstove Chimney - Best Route Out

I'm in western New York State - snow country. I recently built a two-story, three-sided addition on the back of my c.1835 farmhouse. We insulated it with high-density closed cell spray foam, and plan to complete the job with unfaced batt insulation on the interior. We are installing a nice soapstone woodstove on the west wall, and have to chose between two routes for the stove pipe, each with its own pros and cons:

1) Run the pipe up through the second floor into a chase just inside the exterior wall, and up and out the roof (the foam insulation was sprayed to the underside of the roof decking, between the rafters). We would need a couple of 45 angles to direct the pipe where we want it to minimize disruption to the bathroom layout above - otherwise it's basically a straight run up and out.

2) Run the pipe up about six feet or so up out of the stove, and then take a 90 angle out the wall. Another 90 angle outside to get vertical, then straight up through the overhang to the required clearance height for the roof. The exterior pipe is well sheiled from view - we're not too worried about how it looks.

There are differences in the cost for the various lengths of the different types of pipe required for each setup. The critical questions on this job are: 1) overall cost;  2) day-to-day performance and draft for the stove;  3) aesthetics inside and outside the house, and 4) air infiltration. It seems like cutting a hole in the west wall for the pipe is inviting cold air into the house as it infiltrates the gap around the through-pipe and collar, and as cold air fills the chimney pipe and sinks down its path into the house. On the the other hand, the pipe going up through the house should draft better, although it too can funnel cold air inside. But there, the way in for cold air is way up in the attic, not in the living room.

Any thoughts on the subject are greatly appreciated.