The Red War was a really big deal, and it had some of the best music and stage design in the game, but yet it is nowhere to be enjoyed. Why not reintroduce it for new lights? To do so, just make it a shortened version so that they don't feel pressured to go through it all, but they are still given a good introduction to all the enemy races and a good understanding of the Destiny world. Right now, you can do Shaw Han's stuff and have no idea what the Vex are, what the Vanguard are, and are going to feel pretty unimportant by the time you get to the tower. It is far more fun for the player to take the role of The Guardian and not just some random guardian that kind of sucks.
Here's what I propose for each mission:
1. Shortened intro mission where we fight through the city's destruction and board Gaul's ship. We then lose the light, meet Hawthorn, and she gives us a shotgun. The ghost has the idea to go to the Shard of the Traveler during the mission. (long mission)
2. We go straight for the Shard and get the light back, meeting Devrim along the way. Our ghost with the light can pick up Vanguard transmissions and we head to Titan. (short mission)
3. We find Sloan who is helping fight the hive, and after helping her regain decrypting tech from the Fallen and clearing out Hive infection, we learn with Zavala about the Almighty (This could be the fight with Mythrax and the Hive knight, but leaving Mythrax alive gives us the decrypting tech). We then go to find the other two Vanguard. (medium mission)
4. We discover the Exodus Black and Failsafe, who fills us in on Cayde and helps us free him from his own Vex shenanigans. Fallen scavengers are on the surface, but the Vex occupy the inside of the planet. (medium mission)
5. We seek out Ikora who is trying to learn about the Almighty by seeking the Warmind. Help her find answers by fighting through Taken that infest the planet and Cabal defending the facility. (medium mission)
6. The Vanguard plans with Hawthorn to take the city back, but the Almighty has to be dealt with before that can happen. We are sent to invade the weapon and take it down. (long mission)
7. We now fight through the city to confront Gaul and defeat him. (long mission)
Not only is this only 7 missions (Bungie's number) compared to the previous 17, but it also introduces new players to unique places and allows them to experience the vastness of Destiny's universe. They don't need to do every single old adventure, but introducing them to the Vanguard one by one, as well as the minor characters like Sloan and Failsafe allows them to feel that the world is alive. This would also give the players enough time with each enemy type to get a general grasp on who they are and how to fight them.
We could have the new guardian gain exotics that mostly everyone already has for some of the missions.
Mission 1, Hawthorne gives you armor (Titans choose from Hallowfire Heart, Doomfang Pauldrons, or ACD/0 Feedback Fence; hunters choose from Orpheus Rigs, Young Ahamkara's Spine, or Lucky Rasberry; and warlocks choose from Wings of Sacred Dawn, Crown of Tempest, and Skull of Dire Ahamkara)
Mission 2, find Wardcliff Coil
Mission 3, find Coldheart in the Arcology
Mission 4, find Sturm and Drang near dead Exodus Black crewmembers
Mission 5, find D.A.R.C.I. in the facility
Mission 6, find Skyburner's Oath aboard the Almighty
Mission 7, reward the guardian with The Traveler's Chosen
All of these are Red War exotics except for the last one, which is just fitting since you start out with the broke version.