The ESP Guitar Company

Master of puppets

Sanitarium is still 1 of my favorites

nem

if you want something easy do nothing else matters

ride the lightning

If you learn how to play One you probably can play a lot of stuff anyway

Benefits to multiple songs on this list, but my two favorites: 

Sanitarium (Welcome Home): very easy intro riff, and super rad chorus lick as well. The solo is on the easy side as well, so this may end up being the first Metallica song you know all the way through. 

Master Of Puppets: The intro is entirely down-stroked, which will strengthen your arm unlike anything else. Mick Thomson from Slipknot recommends every guitarist learn this song as well. 

Just learn all of them, you've got the time.

MoP is good exercise, Memory remains is fun so is Enter Sandman

master of puppets is the most famous

master of puppets is the greatest down picking exercise ever

Learn some slayer and testament instead

Creeping Death will improve you a lot.

Seek N Destroy is really fun

master of puppets!

Many begin with For Whom the Bell Tolls

If you want to get better while learning, do BATTERY! =)

All the Metallica songs

For something pretty easy, do Enter Sandman. If you want something a little harder then that, do Orion. For something hard but amazing, do Master of Puppets.

Entersandman:-)