It depends what you like. Metallica has a range of songs not all of which are too metal. They have some “sellout” albums and songs which grow onto you with time.
My personal favorite Metallica tunes are Motorbreath and Orion (instrumental). Plus classics are of course Four Horsemen, Creeping Death, Battery, Master of Puppets, Enter Sandman, One, Fade to Black, Blackened. These are a must listen.
Pure aggressive thrash from them: Damage Inc, Whiplash, Metal Militia, Fight Fire With Fire, Spit Out the Bone (new).
Ballads: the Unforgiven, the Unforgiven III, Fade to Black, Memory Remains, the Day that Never Comes, Nothing Else Matters
Country: Mama Said
Cheesy metal: Fuel, Aint My Bitch
Slow and heavy: For Whom the Bell Tolls, devils dance, Sad But True