The two most important lines are the short standard leash and the 33 foot tracking line. These are the leashes that will be required when you trial your dog. The short leash must hang loosely when connected to the collar, and should be small enough to conceal or be able to be carried over the shoulder (top left to bottom right).
My preference for the trialing short leash is 5/8 inch wide, 3 foot long leather.
It has a knot in the end so it doesn't slip through my fingers but no handle.
For the tracking line it is important that the line be light, and non-slip.
I love my 1/4 inch coated rope from Palomine Lines. It is coated with Biothane and doesn't get clogged with dirt or heavy when it is wet, and it does not slip through my hands. Biothane is widely available at various online stores and tack shops.
How to Leash Train your Puppy!
You may have to try several different types of line for tracking until you find the one which best suits you.
For general walking and training all phases, I use various length nylon lines.
Tubular nylon is the best as it does not burn the hands. We use tubular climbing lines from REI, we use 5/8" and 1" thicknesses.
Our long lines for protection are typically 1" x 15 or 20 feet.