It all depends on the construction techniques you decide to use. Wedged tenons can be managed with turnings or tenon cutters and drilled holes. Tapered sockets can be managed with tapered reamers and tapered tenon cutters. Try Lee Valley tools for some of the specialty tools if needed http://www.leevalley.com/default.aspx
you can’t go wrong with a good Stanley no 4, or no 5 plane, in addition to a spoke shave or draw knife. These tool would allow you to do a good portion of your flattening and shaping for a stool. You may also consider a good panel saw (approx 5-1/2 pounds) or back saw (14-16 points) for stock prep.