One reason the Spanish had problems and lagged behind was inflation from all that gold and silver. They were suddenly cash rich and struggled to cope from an economic perspective. There's a very interesting podcast from the BBC series, 'History of the World in 100 Objects', that examines this. Look for the episode on 'pieces of eight', here.

Bernard Bailyn looks at Europe's view of the New World in the 1600's, in his book 'The Barbarous Years'. This may be a little late for the time period you're looking at, but essentially there's a complex relationship with the New World - pagan and savage in some respects, but also recognisably sophisticated in other ways. For instance, he explains how Elizabethans viewed North Americans as primitive and 'at an early stage of human development' but not necessarily savage like the so-called 'wild irish'. The Incan and Aztec civilisations were considered more sophisticated than this though.

I'm not sure what the average peasant thought of the new world, but for those with a sense of adventure, it represented entrepreneurial potential. The new world was generally considered be culturally inferior to Europe, and ripe for the picking, essentially.