Room Acoustics

Carpet is fine but ditch the egg carton foam. That egg carton is not fire proff and if your looking to make an impression with the ladies forget the foam on the wall. I would look for something suttle such as Michael Green's room tunes for the corners and work around that. I say less with room treatment is best than to much.

Try Cork Wall tiles.
However the objective of room treatment is never to sound proof a room unless its a studio. The priorities are the reflection points and corners. Lots of information available on the net. see www.rivesaudio.com on room treatment.

Very little can really be done in an apartment to soundproof a room since most of the trouble comes from the low frequencies that, quite frankly, get right into the structure of the building. Hard to imagine how you could build a second shell inside the room that would be decoupled as much as possible from the building itself. Absorbing materials are all fine, except they will merely soak up the mid and mostly the high frequencies. An array of acoustic panels and sound traps would "tune" the room, but I am afraid would not alleviate the leakage that would elicit complaints from your neighbours. Low level listening is probably a must in your case. A neoprene gasket around the doors would help as you would be surprised how much sound gets out through such openings. If the building is not sound-proofed as it is, you will spend a lot of effort and money and will still, I would think, wind up with complaints from neighbours.