The Anti-Material Rifle or Gauss Rifle, depending on if you're better with Guns or Energy Weapons, plus armor piercing rounds and a sneak attack critical will make those giant lizards deader than dead. Going in guns blazing will only get you killed unless you've got a high Explosives skill and a Grenade Machine Gun, which is an expensive way to go about it, but feels more badass than slowly sneaking around the rim of the quarry for sniping. But whatever weapons I end up using, I usually put off any deathclaw slaying until my level is somewhere in the twenties, so I'd recommend the same for you. Also, stop skipping through NPC conversations. There's useful info in the things they say, and if you don't stop and listen very once in a while, you'll just be stumbling aimlessly through the game and your experience will suffer for it.