DavyJones is very close to the mark.
I installed my own two years ago, similiar setup to heat a slightly bigger area. My flue went up the outside wall.
Small Mulberry (Joyce) wood burning stove was around €450. Marble base was around €150. Stainless double walled flue. approx 6meters with a couple of bends came to €1400 (MI-Flues Summerhill, Meath). Installation was fairly simple and took around a day. Total without labour €2000...