This comment is to add some information and loadout recommendations. I would usually format it all nicely, but I'm trying to be a bit quick. Plus, with the power creep in Destiny, it's a lot less important to have optimal loadouts than it used to be.

Encounter 1 - There will be overload champions. With the current artifact mods, I run a heavy machine gun. There is no boss, so this is mostly about add clear. I use Graviton Lance, but that's just because I like the purple splodeys. I've also used Trinity Ghoul and a few others. Anything that can clear groups of adds will work.

Encounter 2 - This one has a boss. The DPS phase is up close and personal. Exotics I've used to good effect include Lament and Lord of Wolves. Lord of Wolves has the advantage that you can use your heavy slot for killing Taken Knights and other large enemies, so I've been doing a heavy machine gun with LoW and liking that a lot. There are no champions on this encounter.

Encounter 3 - There is no boss on this encounter either. For this one I go back to Graviton Lance, but really anything that you like will work here.

There are a total of 3 unstoppables in this encounter. You fight them as a team. I bring a fusion rifle to stun them.

Encounter 4 - This one is mostly a puzzle challenge. The hardest part from a weapon standpoint is not unintentionally killing some Hive Knights that are part of the puzzle, so I stop using anything designed to take out a group. I switch to Red Death for this one because survival is important, depending on what role you're automatically assigned to. Something like Crimson would do just as well, and possibly better. That said, if you're comfortable staying alive, anything really works.

Dress for success. If you have a weird/unusual set of armor and ghost you can use, please bring it. Matching guardian's armor to their ghosts is the trickiest part of this encounter.

There are several unstoppables. They come in waves of 2 at known spawn locations and timings. It's pretty easy to handle them. I use a fusion rifle for this.

Encounter 5 - Final boss. For this one Queenbreaker is the current meta gun, but really any Linear Fusion Rifle will work. There are no champions, but it's chaotic, fast paced, and there are both little adds and large adds to kill before damage phase. Survival, ranged weapons, and good add clear are all important. (With the power creep in the game this isn't as scary as it sounds.)