A stiff line is better than a soft line because it does not tend to absorb the twist from the casting action. This can be checked by winding some line around your finger and releasing it , a stiff line will unwind quickly back to a semi straight format where a soft line will not unwind easily and will retain some of the coiling from being on your finger.
A smaller diameter line will always cast better than a thick line so always use the thinnest line you can get away with. If fishing around rocks you will need to use a thicker line to avoid damage from sharp rocks and oysters etc.
Breaking strain of your line is dependent on your rod size and action and the weight of rig you are casting. Most rods usually are marked with the maximum breaking strain of the line recommended by the manufacturer. It is also common to use a “leader” which forms your rig of a heavier grade line than your line on the reel basically to protect the rigs near obstacles on the bottom where you are fishing and from the fish’s teeth should they bite above the bait.
When casting very heavy weights on a strong rod some times a “shock leader” is used which means the first say 10 meters of line off the reel will be a heavier line to get the cast away but after that you go back to a thinner line to get the best distance into your cast.
Please also read our comments on the web site about the correct use of swivels to avoid excessive line twist.