For pure distance, the larger the shot, the longer the range (downside is you reduce the # of shot available).

For pure distance, a slug would be your best bet (with the saboted ones having the advantage over the Brenneke type (attached wadding) which are better than the hollow base rifled type, which are better than the old "pumpkin ball" (single round ball) type.

As far as killing paper goes, you will have to try each type to see which one your gun prefers (BTW, the sabots really prefer a rifled barrel)

For deer, buckshot is considered a 50yd load, slugs are considered 100yd capable (a good rifled barrel with a sabot load it likes will reach out 125-150yd and still be effective)