OP has it wrong: the story of the Silmarillion can instead be summed up as:

Be he foe or friend, be he foul or clean

Brood of Morgoth or bright Vala,

Elda or Maia or Aftercomer,

Man yet unborn upon Middle-earth,

Neither law, nor love, nor league of swords,

Dread nor danger, not Doom itself

Shall defend him from Fëanáro, and Fëanáro’s kin,

Whoso hideth or hoardeth, or in hand taketh,

Finding keepeth or afar casteth

A Silmaril. This swear we all…

Death we will deal him ere Day’s ending,

Woe unto world’s end! Our word hear thou,

Eru Allfather! To the everlasting Darkness doom us if our deed faileth…

On the holy mountain hear in witness

and our vow remember,

Manwë and Varda!"

As someone who has not (yet) read the Silmarillion, what are the three pieces of good?

Imagine a 80 minute animated film of just Beren sneaking into Angbad and stealing the silmaril from Morgoth's crown.