But did they come out of octagonal stock?
No they came out of the same round stock shape as I make my hex bolts out of as you cannot buy the right size BA Hex stock these days.
4 jaw SC chucks are a nice to have, if you have the money you can buy one. If you are short of money start with a four jaw independent chuck and a face plate - it will do everything you need but take longer to set up. Then you can choose if you want to buy a three jaw or four jaw self centring chuck - when you do you will notice that the four jaw ones are more expensive.
It is always recommended that you protect soft metals when you hold them in a chuck to prevent the jaws marking the material when they are tightened.
Jo
P.S. Cheap chucks don't remain accurate as long as better quality more expensive ones