you have plenty of options, First and foremost without seeing pics I can of assume, but if your going to land a stove down there your are in a non combustible area, with basement installs the first question I have is do you get water down there? if you do, please consider building a hearth using cement blocks to keep the stove off the ground, using blocks makes the job real easy, plus you can veneer or tile the top to make it look real nice, the back wall closest to the stove, can be veneered also, the stove pile, again assuming that your going to go outside and straight up should be double walled with minimal elbows 90 deg bends, elbows restrict flow there for decrease draft. The wall thimble should be installed following manufactures spec's, you can seal around the thimble using roxal insulation, or other non combustible insulation, now were the work really starts... I would highly recommend finishing the rest of the walls in the basement using blue 2x4 construction, vapor barrier, and insulation, concrete doesn't hold heat, it absorbs heat and transfers it to another cold area, ie dirt behind the wall. You can seriously lose upwards of 30% heat produced from your stove to the non insulated concrete wall, no fun, in other words take 30% of your total hard worked / earned wood pile and give it to the neighbor because your wasting anyway..lol. But seriously insulation is a must. Other things to consider is what you natural draft is like, do you have large appliances in the basement that will rob your draft ie: dryer, forced hot air system, strong bathroom vent fan, some house have a radon vent, very tight house? You may want to consider an OAK (outside air connection) No moving to the most important part : the chimney, are you going to use an existing chimney or install a stainless triple wall insulated pipe? If you using a prefabbed triple wall pipe just make sure that you run it to the right height, Sometimes running a minimum height will give you a decreased draft and your stove will not function the way its suppose to, if you using an existing masonry chimney, please have it inspected, even with a good inspection install a stainless insulated liner, it will eliminate heart ache in the future and make cleanings a breeze. I wouldn't really worry about going crazy insulation behind the hearth, you can install 2x4 steel studs and roxel or non combustible insulate between the studs then hang cement board over it. Stone veneer it or brick it. That's just my two cents, hope that helps you and good luck, sounds like a fun project.
