I have a basement shop. There's no economical way to do this. In the 7 years of having my shop, I've concluded the following:
1) Spend your money on insulating yr shop from escaping DUST - not noise. Get a good dc, a quiet air cleaner on a timer, and a good dust mask.
Done. The JDC air cleaner's on order and I'm in the market for a dust collector.
2) Do your loud operations during waking hours.
I wish! I have 10 week old twin sons.
3) Try to position your shop under the least used rooms in the house.
That is definitely being done. Couldn't be better. The bedrooms are at the opposite end of the house, and the majority of the shop is under the kitchen, laundry, office and family room. The family room gets NO use since we have a living room. The corner of the shop catches the living room, so I'm focusing my insulation efforts there and in the kitchen which is adjacent to the living rm.
4) Drop ceiling tiles - even the cheap ones, will do a lot for sound dampening.
Fingers crossed!
5) Many people put their dc's in a separate closet that's insulated. IMHO, the low frequency of the dc can be heard only as a low hum from the upstairs floors. It's not disturbing.
That's the plan for the DC. The loud air compressor will be left in the garage and I'm running type L copper hard-piped to the basement shop so I'll have air down there. It'll actually be a slick setup.
6) The loudest tools are my planer and router. You might be best served having these two small tools in yr garage. Both are compact enough to be stowed in yr garage, and can be rolled out into the d-way when in use...?
My planer's a screamer too. Honestly the bulk of my work is woodturning and table saw work. The lathe is very quiet fortunately.