Welcome to the community!
If you want to go through the "learn to play" instructions included with the base set, you'll want to set aside the Law Dogs and Sloane Gang decks that came with the base set. You only need one of each deck. If you want to replay that "learn to play" scenario, you can find the contents and order of each deck here.
Go ahead and break up the other "starter" decks. If you got both the Premium box and a regular base set you should have a full playset of everything even if you don't ever take apart one of each starter deck. The Premium set is basically two regular Base Sets put together, so you have the equivalent of 3 regular base sets.