Which is best single stage gas furance or two stage. What you think about the luxaire climasure 95.5 model

What is the purpose of puttinf a vent on the side of the house.

A two stage unit does offer a small advantage over the single stage for energy saving/comfort but I would not pay a lot more for that option. The vent on the side of the home is probably the discharge exhaust from the unit. It safetly removes the burnt gases from the furnace to the outside air and prevents you from getting CO poisoning. Years ago all most all furnaces vented into the chimney but the exhaust gases now a cool enough to just vent out the side wall of the home.

Luxair is a division of York and other name brands. They have been around for a long time and have no more or no less problems than other manufactures units.