I have a shallow well and the pump is in the basement of the house and it is quire noisy when it is running.
What can I do to reduce the noise, I think some is coming from the copper pipe vibration. I want to build a closet around the pump area and insulate the thing , how much air space do I need to leave for the pump?

Is the pump or the motor that is noisy? It is probably the bearings in the pump. Replace it. You are going to have to replace it eventually, why not now. Masking the noise will not prolong the life of the pump.