I use my 4 jaw self centring most of the time, except when using hex bar.
I have found over the years, all my 4 jaw sc chucks have slightly less runout than my standard 3 jaws. usually less than 0.002″.
I find them just a little more versatile for my personal needs as I tend to use round and square stock more than round and hex.
For a first chuck, I would definitely go for a three jaw, then a four jaw a very close second.
Just as a point of interest, no matter which chuck you buy, get a set of soft jaws to fit at the same time. I won’t buy a chuck unless soft jaws are available for it, and if used correctly, soft jaws can make precision machining a piece of cake.
Bogs