Volt posted above while I was typing with much of the same recommendations, so apologies for any redundancies below..
Keeping the music in the room and external sound out is "isolation", which is different and more difficult than "treatment" of the room intended to improve listening acoustics within it.
Isolation-
Close it up tight as you can which helps at low mid through higher frequencies, as any air gaps represent a path defeating isolation. Not much you can do to isolate (or treat) low frequencies.
Treatment-
Try multiple options to find the best arrangement of speakers and listening position and then work from that as starting point. Arrange everything else around that. Just like recording, position is number one. The most effective "treatment" is reducing the influence of the room as much as possible by using an arrangement with the speakers placed well away from the walls and a relatively close "near-field" listening position to them.
A clean stark room with nothing in it looks nice but is unlikely to behave well acoustically. Lots of cushy furniture, storage shelving, and other stuff of life in the room is all good. Don't worry about clutter, that's good diffusion. Keep as much furniture and bookshelves and stuff in there as you can.
Some stereo test signals are useful. Send mono pink noise sent to both speakers and arrange things to achieve a tight cohesive mono image between the speakers.
[edit- all the stuff above is fundamental and costs nothing. It will improve the performance of whatever playback gear you are using. The limit beyond this is likely to be defined by the quality of your monitors]
Before you go out and buy foam or anything else, play around with thick couch cushions, mattresses, thick layered blankets, thick rugs stuff like that if you wish to experiment with reducing reflections. Anything you put on the walls to absorb reflections really needs to be sufficiently thick to work effectively. The one inch thick foam stuff is only effective at high frequencies, it needs to be more like 3" or 4" thick. Anything absorbent will be more effective if you mount or hang it off the wall with an air gap behind it. If the room needs to be normal looking, you might hang a few carpets, or put 2"-3" foam on the backside of large paintings or wall hangings and mount them off the wall with an air gap behind them.
If you are serious about it, make room response measurements along the way and use that to guide you. That's an entire discussion in itself.
[edit- Use good monitors that you can trust, such that your recordings translate well to other systems outside your own room. This is probably where any money is best spent.]