voyage through parts of space where they will not go through any asteroid belts or meteor fields, and by equipping the starship with a very heavy shield. (Depending on the size of the vessel and the speed it will travel at, these shields can weigh in at hundreds of tons)

Yes, but you can only plan so far ahead. You can't scan for pebbles or smaller debris and there is no radar that can accurately map out asteroid belts millions of kilometers away. Even if it could, the turn radius would be too high and it would require to great a force to decelerate or turn in the first place.