Hawkmoon and Praedyths in Iron Banner has been good to me

It just depends on what you got to do. If I do the sword on Crota hard my set up is Red Death, LDR5001 with armor piercing and Hunger of Crota. If I get a mask of the 3rd man someday the Hunger will probably make place for a Gjallarhorn and the Red Death for Fang of Ir Yut. I most of the time use Fang of Ir Yut/ Vision of Confluence/ Word of Crota, Icebreaker/ legendary fusion rifle, Hunger of Crota/ Gjallarhorn for everything. If you have Hawkmoon and a very good legendary sniper you can use that, but I personally would go for a very good legendary scout rifle (f.e. saterienne rapier, badger ccl, b-line trauma, another nitc) combined with the Ice Breaker. Altough I do like Hawkmoon.

For PVP I love using Red Death w/ Secret Handshake for some Mid-Range/Close Quarters Action. For Strikes I usually go Red Death and a Sniper or Crusader I and Ice Breaker For normal story missions or just patrolling I find that any weapons you can have fun with will work well. For Raids it largely varies by your play style, frankly I think Hawkmoon+Sniper is the best all-around set for raiding that you listed. Good Luck in your Travels, Guardian.

Check out my rumble history on my hunter. Used Red Death and Shotty

I suppose it depends on the situation and what you are doing e.g., raid, story mode etc. For pit on Crota's End, I would use Fate Bringer and Ice Breaker. Unless you are running the entire thing invisible which is a possibility especially with Don't Touch Me's equipped. If you like close quarters combat then Red Death and Shotgun is the winner, If you like sitting back away from the action (or if the situtation dictates that then scout rifle and Ice breaker would probably be best. Just my thoughts.