This is a bit of cheat but for the begginer a real blast. As you leave vault 111 you will pass the Overseers office where if you read the overseers terminal it tells you that to pass the time the overseer has been tinkering with a cryogun. however if you try to collect from its display cabnet inside the security cage it will tell you the display cabinet is locked tight and you cant open it however there is a way around this problem.
Go off to Redeocket and collect Dogmeat he will be able to help you.
First you need to get Dogmeat into vault 111 however the game wont let you (dont waist your time telling Dogmeat to go to the lift and stay while you start the lift then join him because he will be removed by the game as you decend into valt 111).
Take the lift into vault 111 as you normaly do move clear of the exit area then open your CONSOLE using the ' for Uk keyboard and ~ on the Us keyboard, type in prid 0001d162 press ENTER then type moveto player and press enter again this will bring dogmeat to your side next make your way to the overseers office and unlock the security door in the security cage (this is a novice leval pick) call dogmeat into the secuty cage select B then select talk (Pc) on your controller and then select can you find something for me then select item, Dogmeat will then recover the cryogun for you good luck.
De Bob G7DME