These days, a new 12" lathe will come with 6 and 8" chucks. You need to be mindful that opening the jaws a great distance might lead to an unsafe condition. A jaw can come out and hit you and the workpiece might be soon to follow. Also the jaw might not clear the ways. Also note that most jaws are reversible and can be flipped the other way to grab the inside of a large diameter pipe for-example.
I tend to think that if you have a lower-powered motor a smaller chuck would be better.
Many 3 jaw chucks are "universal" meaning, the jaws move in unison and you don't need to worry about centering the work because it's done automatically by the chuck. Often times, the 3 jaw chucks are not perfect and cannot perfectly center a piece. Most 4 jaw chucks are "independent". Each jaw must be individually set to evenly clamp the workpiece. It's a manual process that can center a workpiece perfectly. There are times when you want to spin a piece offset and that can only be done with an independent chuck. Also, if you have a thinwall tube to hold, it's better to have 4 jaws (or even 6) to distribute the clamping force.
There are times when a 3 jaw is the only way to go -for example, clamping a piece of triangular or hexagon shaft.
A common combination for folks with lathes that size is to utilize both a 6" independent and 8" universal.
EDIT: Fixed a sentence.