This video from talk show in Canada describes some of the things that can go wrong when you install a drop ceiling incorrectly (RC channels) and how newer materials like QuietRock work in comparison.
It's not too late to insulate. A few years ago, most American homes had no insulation in them. When a homeowner did insulate, it was usually with fiberglass batts. Then along came some better products. One of them is blow-in cellulose insulation. Does it work? I can attest to this: YES. I've used it in walls and ceilings, and it works quite well for airborne noise. If you live in an uninsulated home and you hear your neighbors voices coming through your walls or ceilings, cellulose will dampen that noise or mute it entirely. It doesn't work for all types of noise. But it doesn't eradicate impact noise. You might still hear the sounds of someone walking across a bare hardwood floor with their shoes on, for example, or hear wall-mounted cabinets opening and closing. There are other solutions for that, and by combining different solutions you can control most structural noise and create more privacy. Low cost Blow-in insulation is inexpensive. You can hire a