Sound proofing floor

Pedrillo,
I am in the middle of a sound proofing project and have found the Green Glue web site to be an excellent practical and no nonsense source of information and test results. I would encourage you to read everything on this site before going too far. They discuss a variety of common approaches and solutions and counter some things that seem intuitively correct. Whether you choose to use their products or not, it is very helpful.

Here is the link.
Green Glue

Green glue appears to be the most commonly used adhesive in soundproofing projects. A friend has a Rives-designed dedicated room which used a lot of that stuff.

As someone has already intimated.....is consult with an Acoustic Engineer (not some builder who has done acoustic work).
Acoustics is a science (unless we try to design a Concert Hall where it becomes more of an art), and what may seem logical to the uninformed can often be disastrous.
Putting in another floor is a pricey exercise and you want to do it ONCE and CORRECTLY.

Most of the advice posted above would spend your money for little result.
Sound travels in 2 basic ways....STRUCTURE BOURNE and AIR-BOURNE.
The trick is....the air-borne can become structure-borne and vice-versa.
Unless you TOTALLY decouple your new floor from the old, the STRUCTURE-BORNE sound will travel through.
Only an Acoustic Engineer can visit your situation and advise on the possible solutions.