The same thing they look for in all hunter classes: looks, movement, rhythm, way of going, style of jump, lead changes, striding, etc, etc.
However, has he done any hunter shows, or practiced over full courses? If he hasn’t, I would not start him out in the pre-greens at 3’, since it is already halfway through the year, and you’ll be breaking his first-year PG status. Most of the horses you will be showing him against will be pretty well into the swing of things. I personally would start him first in the 2’6" Baby Greens, and see how he does there for a couple of shows, and then if he felt really confident move him up to the 3’ PG.
Do you plan to show him, or are you going to have a pro ride him? If a pro, I would ask for their opinion on what division would be best to start him out in, and they can give you an assessment of his abilities/likelihood to succeed in the hunter ring.