... to my way of thinking are material, length, configuration, and proportion.

Materials are quite varied, and other members are much better equipped to speak about them than I am. Personally, I prefer thread furled leaders, and my thread of choice is Danville 210 Flymaster Plus. Uni 6/0 seems to be a very popular thread for furled leaders. Some monos and fluoros are also pretty popular.

Length is discussed in terms of starting length and finished length. It seems most people twist the material to the point that the finished length is about 90% of the starting length. The jig that I use generally produces a finished length that is about 85% of the starting length. I really don't get too excited about this aspect of furled leaders, because a few inches more or less won't have much, if any, effect on how the leader performs.

Configuration refers to how many strands of material there are in each section of the leader. What seems to be the most popular configuration is a 10-8-6 i.e. ten strands in the butt section, eight strands in the mid section, and 6 sections in the tip section. With finer materials, e.g. Uni 6/0 vs Danville 210 which is closer to a 3/0 thread you might want more strands in the configuration, say a 14-12-10, or if you want to have a heavier duty leader, to fish large nymphs under an indicator, for example, you might use the 14-12-10 configuration with the 3/0 thread.

Proportion refers to the length of each section as a percentage of the total length of the leader. My own preference is for proportions 40% butt section, 30% mid section, and 30% tip section. The more sophisticated folks probably have any number of configurations they use to achieve a particular performance characteristic.

You can make furling leaders as simple or as complicated as you want. Parnelli, and some others, are really into the "science" of it and have done a whole bunch of work developing different leader formulas. That works for them. For myself, I just like to keep it as simple as possible and typically fish a single leader material / length / configuration / proportion on all my rods for just about all the fishing I do.

John