The three things the pilgrims built after their arrival was

fortification, church, homes

Their own house for survival, Protection around the houses for being safe from external threats and their own farmland or garden to provide them the required food.

Explanation:

The Pilgrims traveled to find a permanent land for themselves and build a good life. They wanted to practise religion as per their own choice and build a bright future by earning money.

The Pilgrims built their new life by first constructing a house for themselves. The initial houses had thatched roofs but later were replaced by planks. Each house had an area for fire which was the only source of energy.

The house was accompanied by its own garden where vegetables were grown.

Their houses were surrounded by a fence for protection.