build a room in a room or sounddeaden exsisting room???

Hi, I am looking for advice on what I should do with a room in my apartment that I want to turn into a music studio. Here are some details It is on the second floor There is someone living beneath me his kitchen is beneath the room that im making a studio The outside wall of the room has two windows and is facing my neighbors house The left wall is against my living room On the right wall there is a closet ( about 10'L x 3'w x 8' h) and then that wall is against my kitchen The other outer wall has a hallway separated by my wall and then my neighbors wall that lives to the side of me. Hope that makes sense I want a room that I can practice singing in and playing guitar/keyboard without worrying if my neighbors will hear it. I was thinking about turning the closet into a sound booth Making a separate soundbooth in the room or deadening the sound in the room and using the whole room as a studio. Im just wondering what the easiest most rational way to go about creating this is and what would be the most logical choice for what type of studio/soundbooth. There are really only three areas im concerened about which is the neighbor below me, the neighbor to my left and the neighbors that live in a house to my right. ANY advice would be greatly appreciated