Whatever you do, build the masonry chimney within the walls of the home (i.e. within the building envelope). Fireplace will draft better and not have the cold hearth syndrome that chimney's built on an outside wall suffer. Secondly, build the structure another 4" thick. I make a living replacing masonry chimney that are typically 4" thick. Masonry chimney's that are 8" thick have far less problems. Tell the masonry to put up 4" block behind the brick or stone your are installing on your chimney and you will limit future masonry maintenance expenditures. Thirdly, make sure the top of the chimney is waterproof with a proper concrete crown and make sure the design of chimney is such that the top of chimney overhangs the body of the chimney like a soffit overhangs a house. The less water that comes into contact with the masonry, the better. Finally, if you can get the masonry to use round clay tile versus square or rectangular, you will be far better off. Square and rectangular flue tiles crack/fail far easier than round ones. Even if it costs a few dollars more, go with the round ones. The masonry will complain that they don't make them anymore but that is not true....it might be a special order, but you can still get them...just make sure they are the right diameter.
General advice. Contact licensed chimney expert for your particular situation.
For years, people throughout the greater Milwaukee and Waukesha areas have been turning to Smoke Stacks, Inc. for their chimney repair and relining needs. At Smoke Stacks, Inc. we believe that attention to detail, professional work, courteous service and honest prices are the qualities that make the difference.