What is a good audio editing software for Mac to remove background noise?

I want to remove some of the background noise from some recordings I have of my college class's lecture that I recorded on my phone. I was curious if there are any programs for Mac that audiophiles would recommend. It would mostly be removing any sharp noises in the background that are distracting like doors closing or people coughing. Also, if it matters, I was curious if there were iPhone apps for recording that would improve my ability to do this other than the built in voice memos app?

Just drop it into Garageband, you should've gotten it for free with your Mac. A standard lowpass or bandpass filter should work, see this answer:
http://superuser.com/questions/106671/how-can-i-use-the-band-pass-filter-in-garageband