Still have my 500 Moss 12 ga. and I use:

3" Whinchester Heavy Load #5's in the Undertaker H.S. that others on this site recomended to me. Bass Pro has it for $16 but found it later at Wal Mart for $14. Did a feild test on a tree at around 40 yards on a plastic bottle and I loved the pattern I got not only on the bottle but the tree as well.

Get a Hastings extended choke tube, and 3 inch with #4 shot.

One of the best lead shot 40 yard patterns I've seen, (not a Hevi-shot load), was fired from a Mossberg 500 pump. The choke tube was a Hastings non-ported extended turkey tube, in a .665 constriction, using Winchester High Velocity, (black box), 3" Turkey loads of # 5 shot in the 1 3/4 ounce payload. The choke tube's affordable, (about 23 dollars), as were the shells at under 10 bucks a box. A very lethal combination in that gun. #6 shot in the same load works well too, but you give up some down range energy with the smaller shot size. I'd stick with the 5's.

Extra full choke, 3in 6 shot

get a remington........there problem solved!! get er done!