The easiest way is the only way. Run crota on normal and hard no other way to get them

Run through the entire raid, don't skip using a friends checkpoint. Chests and Deathsinger can only be looted once per week. You cannot loot them on Normal and Hard, as they only drop once. Once you have all the armour and weapons you want, keep running the raid and scrap the extras for more energy and shards.

The easiest way I have found is running multiple characters through Crota's End on Hard Mode. Then prioritizing all the materials earned to a weapon/armour piece you want upgraded. Hope that helps.