To understand the relationship of the new world to the old, I would suggest reading the following (in the order given):

Guns, Germs and Steel: The Fates of Human Societies…by Jared Diamond
Guns, Germs and Steel (amazon affiliate link)

1491: New Revelations of the Americas Before Columbus…by Charles C. Mann
1491: New Revelations of the Americas Before Columbus (amazon affiliate link)

The Other 1492 : Ferdinand, Isabella, and the Making of an Empire (The Great Courses)…by Teofilo Ruiz
The Other 1492 (amazon affiliate link)

1493: Uncovering the New World Columbus Created…by Charles C. Mann
1493: Uncovering the New World Columbus Created (amazon affiliate link)