Treating the old application as the spec for the new one is usually not a good idea. Define the problem(s) the new application is trying to solve instead of trying to copy the behavior of the old application. This is important for both developers and users. (http://www.chadfowler.com/2006/12/28/software-as-spec)

I like tackling the tougher parts first as assumptions usually conflict with the real world and the design will change once you start building and testing.