Soundproofing for the wife makes sense, but not the baby. New babies like it loud, it's very loud in the womb. Stomach going on, heartbeat. My daughter would sleep through the TV, or the vaccume or anything. When we wanted her to sleep we turned her clock radio to the white noise between channels and turned it up. There is a point almost loud where it's like a switch, she went right to sleep.
I would recommend that you don't make it quite in the house for the baby, because sudden noises will wake her/him. Play the radio for the baby. See the video "The Happiest Baby on the Block", it's amazing and works. You can pick it up at the library. Best investment of 1/2 hour you could make with a new baby.
That being said, the first few months are mentally exhausting, and you will be tired. Be real careful about tools. There were many times when I couldn't think straight. It's like being drunk, you think, oh I'm fine, just a little tired, then you lose a finger for the "Quick little cut".
For soundproofing I used to use 1 inch thick blue board. I used to live in a neighborhood in college and used to throw parties for 60-70 of my dearest friends. This old house had single pane windows. I cut blue board and pushed it into the window cavities, it reduced the outside noise dramatically. Instead of 50 ft, I had to get to 10 ft.
Also, my neighbor had a theatre room put in, and they put noise blankets on his heat ducts. The stuff the put in your car to keep engine noise down. The installer said that the speakers would rattle the heat ducts and make rattle sounds upstairs.
For what it's worth.
-John