Buy Rod Gervais’ book on home studio construction. Pretty much everything you need to know is in there in plain terms. The bible of the amateur studio building community.
You should buy soundproof foam from Guitar Center. Foam only damps high frequency reflections. Making the room sound deader but not reducing noise on the outside at all. Most of what gets out (and is most difficult to stop even with construction), and annoys neighbors, is low frequency noise. Particularly bass drums.
Real acoustic foam is fairly expensive because it is flame retardant. Hanging mattress pads on the walls is an invitation to another Great White fire trap. Better is rigid fiberglass insulation. Which can burn but is much harder to ignite. Those shapes you see on the walls of movie theaters are made of this.
Isolation of noise takes exactly that. Physical isolation or decoupling of the inner surfaces of the room from the structure or outer surfaces of the room. Lots of ways to do this with varying degrees of effectiveness. From resilient channel behind the drywall (you have to remove the existing drywall to do this) which is what home theaters and hotels do, to a full on independent floating structure inside the existing space. Which is what real recording studios do. The first gets maybe 10 dB of isolation and much less in the bass. A correctly done full on studio can get up to 50-60 dB of isolation. A band or decently loud drumming can be between 95 and 115 dB.
Now think about what you really want to do. Do some research and costing out alternatives.