Sound Insulation- how much can it help?

Buy a home.

What you seek is impossible.

Sorry.

You cannot the violate laws of physics and the propogation of sound waves through walls/floors is one.

Wall to wall style carpeting can work wonders applied to walls, doors and ceiling. Almost relevant, we used it once to insulate a wood frame garage for band practice. The best is heavy wool pile, very plush and heavy. You may need to screw some kind of lath to your walls to hang it. On the downside, with the bodies and equipment in there it got really hot sometimes! The police still came but after witnessing our efforts to protect the public and securing our verbal agreement to respect the 10 o'clock noise ordinance we did OK. From an equipment perspective, stand mounted speakers that trade finesse for pure grunt may be a partial solution.

I agree, you can only limit the sound to a certain degree by using these "soundproofing" methods, and it sounds to me like it will never be enough in this circumstance.

You need to either be flexible enough to listen at low volumes during these time periods, or you need to get into a single-family home.

Well, you have the answer. Someone asked our company what we couldn't do one time. I said "we haven't figured out how to break the laws of physicis." Herman has already pointed out--that's what you're up against. We're about to publish a paper on sound isolation (hopefully I'll finish it this weekend). The basic problem in an apartment is that there are many structures in common. You pointed out one wall, but what about the ceiling? The concrete slab? The may all have the same structural components. You play loudly and the sound travels through this structure to the next room. Is it impossible to isolate these issues? Technically no--it can be done. Practically however is a different question. It would mean doing things pretty crazy like ripping out all carpet, putting up new walls, ceiling--well you can see it's just not at all possible in the real world sense.

Now I am going to digress to something I saw at CES this year. It was a headphone system that used Stax headphones and an infrared head tracking device--bear with me here. Basically the headphones were calibrated with a full 5.1 system. You put microphones in your ears and listened and did things like turned you head in certain directions. All the while the pink noise coming from the system was being recorded. Then you take the mics out and put on the headphones. You could move your head and got the same kind of enveloping feel as you did from the 5.1 system. For comparison you just took the headphone off, they would turn off and the real 5.1 system would come on. With matched volumes this was pretty incredible--I was amazed out how remarkable the processing was and they have only just begun--it will likely improve more. Anyway, if this comes to market it could solve some issues like this.

This is why people like myself hated living in apartments and finally moved into a house some years ago... I couldn't stand other people's guitars, sterios, loud tv's, etc. coming thru the walls, floors, ceilings, etc.
Once you move into a house, however, then you have the neighbor booming his music out of his car/truck in his driveway while he works on it or washes it.. coming thru the walls, windows, etc.. it's hard to get away from noise.