Hang the ceiling gypsum board on resilient channels. You can also add some fiberglass thermal insulation to reduce sound that gets through cracks and padding under the floor finish above. Some advise even more refinements but the channels will make the biggest improvement.

Here is a link that might be useful: resilient channel installation

Alternative solutions are dampened drywall, Green Glue, Quiet Floor or equivalent and Quiet Wood.

Avoid potlights and other penetrations.

There is also an open cell foam insulation that works quite well in conjunction with the resiliant channel method.

"You can also add some fiberglass thermal insulation..."

Fiberglass sound insulation works a lot better.

ROCKWOOL

Called ROXUL AFB (Acoustic Fire Bats) in the States.

This stuff is designed for two things. And only 2 things.

Sound & Fire.

It substantially reduces transmitted sound, and also is a substantial fire barrier. It withstands over 1200 degress. So it slows down the spread of a fire quite significantly.

I put in Roxul or Rockwool, on a Remodel that we're finishing up. Between floors. It made a huge difference.

I would also recommend getting a book on stopping sound... a whole bunch of stuff (which we didn't for the most part do...) for proper sound control - needs to be done. For example, be sure to insulate between any door jambs and the wall. Don't just let drywall cover the 'space'. Material exists to insulate heating ducts for sound... Heat ducts like to help sound bounce all over. Myron Ferguson wrote a book called 'Drywall'. His latest revision 3rd or 4th - has a section on Sound Control - since he is just learning about that...

I'm not an expert, and neither is he. But if your doing a major remodel, and are concerned about Sound - now is the time. So do some research, or hire someone who knows what needs to be done.

But just Roxul stuffed into the ceiling joists and between the door jambs - would help a tremendous amount. And that is easy to do for a DIY.

Roxul or Rockwool is itchy - just like fiberglas - when your installing it. But it doesn't have fiberglass in it. (I think that's correct, not quite sure...) KNOW it has shredded rock, and metal slag... I really recommend it for the Sound and the increased Fire safety factor. Available at some Hardware stores. We purchased what we used from a local lumber yard.

Here is a link that might be useful: Sound and Fire insulation

Following Rockwool's link for the states takes you here:

Hope all this helps. While your doing this major remod .- and planning on having more children - do something else as well...

Put in hardwired (connected to house power); 9v battery backup protected; Fire and CO detectors, interconnected. You might be quite glad you did sometime...

Here is a link that might be useful: States info on Roxul

Not to be contrary but an acoustical engineer once told me that the difference between fiberglass thermal insulation and "acoustic" insulation could not be measured in the field so it was better to use the cheaper stuff.

Many acoustic insulation companies clain "superior" sound reduction but to my knowledge none offers any field testing as evidence.

The Canadians are way ahead of the US in the testing of building materials. The tests linked below indicate that filling the floor cavity with fiberglass batts, blown-in acoustic insulation, or blown-in cellulose, produces essentially the same levels of sound resistance.

Here is a link that might be useful: floor testing

"Not to be contrary but an acoustical engineer once told me that the difference between fiberglass thermal insulation and "acoustic" insulation could not be measured in the field so it was better to use the cheaper stuff."

He is wrong.
The acoustical stuff is packed much denser that thermal insulation.

I build rooms that must pass sound attenuation measurements.

Steel studs, double staggered layers of 5/8 drywall on both sides, acoustical insulation, sealing of top and bottom plates to slabs and roofs, sound seal door frames and drop seal doors, and white noise generators near the doors are just some of the things used to limit and mask sound.

EMI attenuation is required also, as well as physical protection (#9 expanded steel mesh in the exterior walls welded to the studs).

I've designed recording studios, computer chip clean rooms, and concert halls but none of that detailing would be appropriate in a home. I would be interested in seeing test results in light wood floor/ceiling assemblies.

Sound isolation is sound isolation.

How much you want (or need) depends on your budget.

Impact noise from footfalls is usually the hardest thing to isolate in light construction.

Wood framing does not have the mass of material to damp out footfalls.

There are a number of standards writing organizations that have detailed methods for achieving various ratings of walls, but floors are still a weak point.

Resilient channel can help decouple the finished surface from the structure, but unless you use heavier than minimum drywall there is still not that much mass present to damp transmitted vibration.

It also quickly gets into the problem of needing stiffer channel to carry extra weight raising the coupling.

A separately supported ceiling (not tied to the floor structure above) will achieve the desired isolation, but at a significant cost in materials and loss of ceiling height.