The Separatists, also known as the Pilgrims, came to North America primarily to pursue religious freedom. They sought to separate themselves from the Church of England, which they felt was corrupt and not conducive to their beliefs. Their goal was to create a new society where they could practice their religion freely without persecution.
While some of the responses mention the desire for gold or adventure, the primary motivation for the Separatists was indeed to establish a community where they could worship as they chose. Therefore, the most accurate response is:
They wanted to separate themselves from everything English and start over.