Sound deadening can be achieved in a number of ways, but essentially, you want the sound waves to be absorbed by something rather than rattleing around in your sink. You can spray the sink with undercoating material, (like for a car, just protect the lip around the edge), or you can add adhesive sound pad to the back, which any car stereo shop would love to sell you for far less than 200 bucks. They stick it to the panels inside your car doors to deaden the sound of the car, making the stereo sound better.
As far as sinks themselves, the smaller the gauge number, the stronger, and heavier the sink will be. If you are going for a porcelain finish, go with a brand name, like elkay or american standard, or the like. Be aware of your plumbing issues in the wall beneath the sink, particularly the elevation of the waste line, which could effect the depth of your sink-garbage disposal combination. In addition, consider your faucet and spray nozzle-dishwasher vent stack needs in considering the number of holes you will need in the sink back.
Lastly, scan the postings for counter top issues. The worst thing you can do is install the top, and discover you made the self-edge hang down so low you can no longer open your drawers. When you install the subsurface, screw it in from the bottom, not through the top. You'll understand why when you go to take your current top off. If the top doesn't come off easily, chances are you've missed a screw. Don't fight it, or you may damage your cabinets. Use a saw to cut the screw if you can't get to it, or drill it out if it was sunk through the top.