We've gone into detail about the subtleties recruiters look for at other positions, but the qualities a punter needs are pretty obvious.
Programs look for a player with a strong leg who can get good hang time and good direction on his punts. The player's ability to put the ball where he wants to can sometimes compensate for lack of distance.
A punter also must be fairly athletic and have the ability to handle a bad snap, and also hopefully be some type of a threat to run or throw out of punt formation. In many cases, he will also serve as the holder on field goals and extra points. Get-off time is very important for a punter, and most programs would prefer a two-step player with a quick release. A slow, three-step guy will get too many punts blocked.
The best quality that a place-kicker can have is consistency. He must be mentally tough and ready to handle the challenge that a game's outcome may ride on his leg. He has to be able to adjust to all kinds of weather conditions.
Programs want a kid with a strong leg for kickoffs and long-range field goals, though many college coaches will sacrifice long-range field goals for accuracy inside the 40. Because of the mental pressure, you don't see a lot of freshmen making an immediate impact.
Most players at the high school level handle both the place kicking and punting duties, but they are usually stronger at one or the other and rarely handle both duties at the college level.