Soundproof material for a dedicated room

I'm thinking of converting one of my rooms to dedicated audio room. Since it's a condo and there are neighbours to the side of me on 2 sides, I'm trying to figure out what I could put on the walls to prevent the sound going next door. Can I get away with just gluing something on the walls or would it help if I built a wall on top of the existing one and put something inbetween. Looking for something that won't break the bank, but also something that is effective. Waf is non-issue. What soundproof product or materials would you guys recommend?

Thank you all for your inputs
Roxul Safe-and-Sound behind drywall will work well. In the space between studs. See if there's a place called Acoustical Distributors International (ADI) in your area. They will advise you on how to install without glue.
Brano, you are going to run out of money for component upgrades.....LOL
I know...I'm in trouble. I might have to start bartending at night. lol
If the wall cavities are empty, you could have an insulation company blow them full of cellulose. I did all the walls, and ceiling of my room done when I built. It actually helps alot.
Sound proofing is a complex process. Using the proper products is a must, but the correct application of them is critical. You should get professional advice. Sound leaks from any bridge that allows transmission of vibrations - not just from wall surfaces. Sometimes a nail in the wrong place can compromise all the insulation!
The room should be so airtight that you have to take a deep breath, hold it, step into the room to listen, and then exit to breathe again. Anything less is not total commitment to audiophilia. ;)
Using Roxul Safe and Sound is a great way to help soundproof your room. The wife and I just did the media room in the basement of our house that is being built. We added the Safe and Sound to the ceiling from the media room and it was virtually pressed into place. A few areas may need to be carefully placed with caution if you have ceiling lights, make sure you have Insulation Contact (IC) lights in order to use the Roxul in the ceiling and close to those recessed lights, otherwise, you must be at leat 3" inches away from those cans in the ceiling. This stuff made a night and day difference in the room, wife tested by walking upstairs and yelling, could barely hear her. This was prior to the drywall install.

You can get Roxul at Lowes in 16" or 24" OC. The batts are 3" thick, but compress easily.

I also did our laundry room on the top floor. If you cannot remove the drywall, use QuiteRock drywall, anything above the 510 series would help you.

Good luck,
If you are 'serious, serious' it is not time to fool around with any of the suggestions already made. Only lead wall paper will work. Yes, there is such a product, and it is expensive, with professional installation. Children? Forget it. I used this product over twenty years ago to 'silence' a furnace as part of a basement media room. Work well. Also had the duct work treated to cut down on air flow noise. As all have said, it will take trial and error to find the best solution. Your neighbors must be part of the solution.
Green glue between 2 levels of dry wall works well. A separate wall, decoupled from the first is an excellent idea as long as you do not triple leaf. Go to the website for The Sound Proofing Company and read their explanations in Sound Proofing 101. As Microstrip said, it is a complicated issue and many of the simple solutions (insulation between studs) really do not work very well, especially for bass.
I 2nd the green glue recommendation. I used to manage real estate and had a few tenants that used it with great success. It was a very cost effective solution. They suggest using 3 tubes per 4x8 sheet of 1/2 or preferably 5/8" thick drywall with lots of screws...basically sandwiching a new piece of sheetrock over the old wall with green glue between them to form a soundproof barrier. I think the website was of testimonials on their website. I have no affiliation with the company whatsoever, it just worked out very well in the applications that I used it in...
Most of the above suggestions will help; but only help. In order to truly soundproof a room you have to build a "room inside a room"; IOW, isolate the source of the sound as much as possible. This is what recording studios do, and there is a lot of info available on line on the subject. If that is not possible, the most effective way to "help" is mass, mass, and more mass. The green glue/sheetrock suggestion is a good one. Then make sure all doors are of solid construction, and seal very well.
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