Soundproofing is part science, part art. You can end up spending a lot of money achieving results not sufficient to the lifestyle you desire, either wanting to play loud music without neighbors knocking on your door or not want to deal with the sharp walking sound from your upstairs neighbor.
Here are the three most cost-effective strategies for soundproof:
Installing radiant heat with Warmboard
Warmboard has been shown to have sound attenuation with or without concrete. This technique kills two birds with one stone. For the cost of installation, you will have the benefits of radiant heating that evenly heats your home and a much improved sound performance.
You can check out the STC and IIC rating on the Warmboard website.
If your heating system is still in good condition, I recommend simply installing a carpet. Generally speaking, the taller and the thicker the carpet is, the better soundproofing properties it has. Importantly, do install a sound attenuation underlayment. Carpet stores generally provide consultation for free with purchase. And they will do the installation for you too, so there is no need to go through the trouble of finding a good general contractor.
Carpet can be installed on top of existing hardware floors without needing the trouble to rip out the old flooring.
Installing custom doors
With many folks working from home these days, it is problematic for the study to hear the living room's noise very loudly. I recommend ordering custom doors that go from ceiling to floor.