You can work with 1/4", but it's easier to get a more comfortable handle with 3/8". Pretty hard to round over 1/4" very much, where you can 3/8" with ease.
Once you have it rounded you can make it much thinner and still retain the rounded shape, if that's what you want.
Curves and rounds feel much more natural and comfortable in the hand than angular, flats, points and edges where they don't belong. Look better too, at least IMO.