What is the brand type of skimmer? Or are you building one from scratch?
We could be talking about two different disctinct skimmer designs. One is called a downdraft (Aqua C uses this design) where a "jet" nozzle forces water into a column of bio balls or other media to cut bubbles into small fine micro bubbles. This jet nozzle can be a proprietary design (can't buy them) or is simple made by heating up PVC and shaping it into a clover shape.
The beckett style skimmer uses a Beckett 1408 (IIRC) foaming nozzle to introduce air into a water stream to produce bubbles.
Both of these designs require pressure rated pumps. Moreso on the beckett. As to how big a pump. that depends on your skimmer. We need a pic, model number, brand, etc. to know what exactly you need. If it was hand built by someone, you need them to tell you what pump they recommend and what nozzle they are referring to.