As said blue pivot steel is the stuff to use. The problem is that you can't easily harden the staff after making – you burn the pivots. So it has to be made from a good grade of steel hardened to spring temper from the get go.
A read of some of Donald de Carle's books might be an idea. The Web has a pdf. Also getting a pair of pivot files left and right (and they are not cheap if new). To check the size I have made a temporary staff from brass, easy and quick.
Usually hand turning with a lozenge graver is the traditional way but I could never get on with that tool and used engraving tools. Experiment, you will surely end up making a few before you settle on a technique that works for you.
You 'can' polish the pivots in the lathe but it is a bit risky. Some sort of support like a Jacot tool makes it less likely to bust the pivot at the last moment (v annoying).
You can also make a simple turns and do the job between centres. Make a little pulley, some cotton thread and a motor and you are good to go.
Enjoy.