No way to know until we know what that chimney is. Lining a chimney isn't a walk in the park. It is a dirty, dangerous job with the working on a roof factor. And you virtually always have some kinds of obstructions and offsets in the chimney.
I called A+ Chimney Cleaners (the company who inspected my chimney), and they were able to tell me that I had a standard clay chimney. Despite my pride hurting, as well as my wallet, I think I'm going to pay them to do the work.
The best price I was able to find for the 8" x 25' liner kit and insulation was $660. A+ said they were a little low on business right now so they would do the install, with parts, for $1,250. If I was going to live here forever, or if adding a wood stove insert to the house added any resale value, paying the $600 difference for someone else to do the dirty work would be a no-brainer, but since I'm going to be heading wherever the Air Force sends me in the summer of 2017, shelling out the extra cash does hurt a bit. I'm not sure if I'll be able to recoup the expense in energy savings over the next 3 winters, and my friend is still convinced we're capable of doing the work ourselves, but the cautious side of me (a very small part of my inner being) says to pay the contractor. My concerns of doing the work myself are:
1) Accessing the top of the chimney. I've been on top of my roof, but the chimney sticks up another 8 feet. I don't exactly have easy access to scaffolding, so I'm not really sure how I would safely get up there to install the top plate. I couldn't exactly stand on the roof like this guy: (see picture)
2) Obstructions in the chimney. It seems like a 13x13 chimney is plenty of space to shove down an approximately 8.5 inch diameter tube, but I have no idea how I would deal with having to remove obstructions inside the chimney, should they exist.
Thanks everyone for the advice and expertise, and please feel free to offer more if you have it. This was my first hearth.com experience and I was very impressed with the plethora of knowledge and willingness to share. I had no idea forums could be so useful.
Damn it...even as I sit here typing this I'm thinking "what if we could just do it ourselves?" Probably always going to wonder that...