Once you've hit level 40 in Destiny: The Taken King, the real show begins. There's a ton of content to dive into, and the game doesn't try very hard to introduce you to endgame. Below you will find a quick guide to progression at level 40.
Focus On Normal Level 36 Strikes
The most efficient way to earn better gear is to run any of the level 36 Strikes available in The Taken King. These are balanced in difficulty allowing you to clear them in a reasonable amount of time without fear of dying. Even for well-equipped players they are considered a great way to gear up.
At present, Heroic Strikes in The Taken King aren't dropping items at a rate that would suggest that it's worth the additional difficulty unless you're specifically looking for a challenge. Though, in the event that you have high Light level gear and are okay with potentially dying a few times, Court of Oryx is an option worth considering.
Your goal should be to run these Strikes, preferably with one or two players who can pull their weight, and quickly clear them while picking up any Engrams that drop. Once done, head back to Tower and decrypt each Engram. But before you do that...
An Introduction To The New Engram System
The Taken King has altered the Engram system in a significant manner. Now, the Light level is calculated upon decryption based on your current average Light level across all equipped items. So, the same Blue Engram will result in an item with better stats on a character with a higher average Light level.
To best take advantage of this, when decrypting several Engrams it's suggested that you do one at a time, and equip an item if it's an upgrade. Doing this you can ensure that you are getting the highest level item from each Engram you decrypt. Every level matters.
Grab a Sword
Swords in The Taken King are very potent, and you'll want to make one part of your arsenal as soon as possible. You have two solid choices. One, you can choose to get a lower level sword and ascend it using higher level items. Preferably, you can work toward one of The Taken King's three incredibly powerful Legendary swords (Arc Edge, Soul Edge, and Void Edge).
The best way to get your first sword is to complete the A Broken Will quest. This is available from Eris Morn in Tower after completing the entire The Taken King main questline as well as a few follow up quests. One of these quests will task you with acquiring five Calcified Fragments.
Once you are on the A Broken Will quest, you will need to obtain 25 Hadium Flakes and 10 Motes of Light. The Hadium Flakes are found inside chests on Dreadnaught (one per chest), while Mote of Light are acquired through daily Crucible matches, loot chests, rare engram decryption, and finishing Public Events with Gold ranking.
Lastly, you will need a material specific to the legendary sword you want to obtain. In the case of Arc Edge, you will need Spinmetal. For Soul Edge you will need Helium Filaments. Lastly, Void Edge requires Relic Iron.
Once you have your Hadium Flakes, Motes of Light, and weapon-specific crafting material, head back to Lord Shaxx to obtain your legendary sword.
Run Dailies and Weeklies For Legendary Marks
Every day that you log-in you should consider running the daily Heroic Story as well as the daily Crucible. This will get you a total of 30 Legendary Marks, allowing you to purchase an exotic every week or so, supplementing the gear you farm through other means. You can also earn Legendary Markes from the weekly Heroic Strike and theh weekly Crucible Playlist.
It is recommended that you do not spend these marks on Legendary (purple) items. It won't take long for you to get a full set of Legendary gear, so you're better off investing for the long-haul by saving for Exotics (yellow).
Ascension Is The Key To Optimization
Using the ascension system you're able to upgrade your exotics beyond their base Light level of 280. To accomplish this, you'll need to be high in average Light level and decrypt Blue or higher quality items that are higher Light level than the exotic you're looking to ascend. If you meet this criteria, you can absorb the power of the item into your exotic, making it even better. This is something you should be doing well into the future as you continue to optimize your equipment set.