The number 60 is not critical at all but seems to be a standard.
The only time you need to stick with 60 is if you are buying TBC bushings which are designed for the 60 degree shape.
However, I never did that.
I just mount my blank between two "points" which stick into small indentation holes that I drill in the ends of the blanks when I initially turn my blank round.
After you have drilled and tubed your blank, the 60 degree centers are a nice fit into the tube ends. But the 60 is not an important number unless you are using TBC bushings in the tube ends.
If you don't use TBC bushings as a guide to the final size of your blank ends, then you need to use calipers to measure the blank end size.
The dead center CAN have "prongs" (often four) on it to dig into the end of a wood blank, but it need not have "prongs".
A steb center has multiple "prongs" or points.
You absolutely need a live center in the tailstock and a dead center in the headstock.
The live center has sealed bearings to allow the workpiece to turn. . It can also have "prongs" or a circular ridge called a cup.
You can get both at PSI although their only dead center is called a spur center and it is much more elaborate and expensive than you need.
https://www.pennstateind.com/store/LCENTSET.html
You can also get at a tool shop or woodworking shop in your locality.
You can also get a live center from
www.ExoticBlanks.com -
https://www.exoticblanks.com/60-Degree-Live-Tailstock-Center-choose-version.html
Here is a listing for a stebcenter, again, more expensive than you need .... just to give you the idea -
http://www.leevalley.com/en/wood/page.aspx?p=49904&cat=1,330,49238
For basic, cheaper products, Harbor Freight or Grizzly should be able to help you .... also Woodcraft and Rockler at higher price.
You can even make your own crude dead center using a big fat spike (nail) (and file the pointed end to make it conical if you want).
