It depends on the mechanical keyboard you get, Cherry MX Reds are pretty quiet but If you're really going for quiet I'd get the Cherry MX Silent keys
Click
HERE for the Silent keys. This is the only keyboard that has them right now as they're really new and Corsair is working with the company that makes them so they can have them exclusively for the time being.
HERE is a link to the difference in sound so you can hear it yourself.
AND If you want SUPER Quiet, I'd reccomend just buying one of the rubber insulated button keyboards like the ones they make for laptops. those are super quiet, just know they wear out much quicker.... but they're cheap so it's not a big deal.
cheap option
ONE, and cheap option
TWO
And finally, I'd recommend learning the audio software you have and finding a way to make your program learn the sound of your keyboard and eliminate those sounds from the audio. it's really one of the better ways if you're on a budget. but if you're willing to spend the extra money, The keyboards are definitely far quieter.