Money spent on a good chuck is worth it. I've had quite a few chucks by now, and I've kept only the Bisons (but I do miss a Pratt-Burnerd, even if it didn't fit my new machine). 4-jaws allow runout to be adjusted by design, but the quality of the chuck dictates the experience you have getting parts set and holding them that way through the duration of the machining operation. In a nutshell, tenth-thousandth movements are easy and predictable in my Bisons. B-line import chucks make thousandth movements unpredictable and fiddly.
Definitely look into your new old stock or open box purchase options, you can save a lot of money that way. Used is okay too, as long as your eyes are keen to the details.