Unless you have it done professionally, no DIY sound treatment will ever be truly 'soundproof'. All you can do is try and mitigate external sound as best you can.
As the world's worst singer, I am paranoid about my neighbors hearing me caterwauling, so for recording vocals (It's amazing the amount of fixing you can do in Celemony Melodyne) I had both problems - I didn't want exterior sound coming in, but neither did I want my racket escaping.
I have tried a bunch of solutions over the years and, in my experience, recording in a cupboard or building a DIY 'booth' produced 'boxy' sounding recordings. After a LOT of trial and error, I found that the best results came from using a room around 9 feet square and hanging as many layers of lightwight bedspreads, lightweight duvets and other materials as possible around the room as I could - the air between the layers of course acting as a noise insulator as well.
I cover the floor in a load of cheap rugs and cover any other hard, reflective surface in the room with something soft and sound absorbent. The ceiling is fine as it is, because it adds a very, very slight response to the sound which I find quite pleasing.
Finally, I record in the center of the room using a condenser mic with an SE Electronics Reflexions filter to a laptop with a solid state hard drive, meaning the computer is pretty much silent as well.
For me at least, the result has been high quality recordings which have just the tiniest amount of 'space' in them, so that they don't sound boxy or completely lifeless, and are perfect for post-processing. And, as a bonus, the neighbors don't hear a word.
Once you're done recording, it can all be folded up and put away until next time.
(Disclaimer: If you decide to try anything that I've written above, it is entirely at your own risk!)