We are going to build a fence around the field with …………….. to breeding sheep and cattle.

Explanation: fixed structurewith a view to + V-ing = for what purpose, for what purpose

We will build a fence around the field to raise sheep and cattle.

The remaining answers:

A. a goal (n) = goal; goal; goal

B. an outlook (n) = a prospect

C. a reason (n) = a reason