What to do next in Destiny when you hit level 20

After completing the main story missions, and strikes you will reach a base level cap 20. In this moment you have to decide what your focus will be – PvP or PvE, because there are different vendors you can get gear from: Class Vendor with Vanguard Armory (PvE), The Crucible Vendor (PvP), or any of three Faction Vendors (PvP).
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For Vanguard Armory you’ll need Vanguard Marks, and the rest require Crucible Marks.

Increase Light level

The stats on your gear help you reduce the cooldown – Strength reduces the cooldown on your melee attack, Discipline reduces grenade cooldown and Intellect reduces your Super cooldown. At level 20, your gear gets additional role – your further leveling is based on a number of Light points on your gear. When you hit base level cap, you stop gaining levels from experience points, but from a new stat called Light available on high quality gear. You need 21 Light points to reach level 21, and every next level will cost you additional 11 Light points.

Since you need a new gear, you’ll have to grind hard mode game content in order to get more marks and reputation and buy Exotic and Legendary items. You’ll be pleased to know that when you upgrade your gear, it will also increase the Light points number on that piece of gear.

You should also know that all vendors require a certain level of Reputation before you can purchase Purple items from them, Reputation Rank 2 for Armor pieces and Rank 3 for Weapons.

Complete Daily Heroic Story Missions and Weekly Heroic Strike

You can start with completing Hard Mode story Missions that you’ve already completed while leveling through the main story, but this time the enemies are more challenging. They reward you with Vanguard Marks, and Vanguard Reputation. You are capped at 100 Vanguard Marks a week.

Weekly heroic strike resets every Tuesday and awards you with 3 Vanguard marks, +150 Vanguard rep and 3 Strange Coins.

Earn Reputation

Vanguard reputation (PvE) rank is increased by completing Strike Playlists, Daily Heroic Story and Weekly Heroic Strike. You can also do Vanguard bounties and Patrols for reputation.

For Crucible Reputation (PvP) participate in the Crucible matches to get Marks and Reputation. Before you start a Crucible match, collect Crucible specific Bounties to increase your Crucible Rep.

Faction Reputation – There are three factions in Destiny: Dead Orbit, Future War Cult and New Monarchy. When you equip a faction item specific for your class – a cloak, mark or bond, that will converts Vanguard rep into Faction of choice Rep, and you’ll no longer receive Vanguard reputation during Strikes, Dailies, Bounties or Patrols.

Joining a faction straight away isn’t the best idea. It essentially means your vanguard marks are useless and any Vanguard rep you already accumulated is put to waste because you can’t spend the vanguard marks. Get the Vanguard to level 3 before joining a faction. The main stat you need on gear after level 20 is Light, and the only benefit to faction gear over the Vanguard gear is that you can choose the other two stats you want to focus on, which has very little impact on how effective your character is. Faction gear is more about building your character around a specific playstyle, which you’ll have time to do once you’re properly geared, however, in the meantime, a new level 20 should focus solely on Light, at least until they get a full set of legendary armor. Faction armor should be a goal for characters who are already high Light level, but who want gear that better suits their ideal playstyle. (thanks DeathCrayon)

Collect Materials

Spin Metal, Relic Iron, Spirit Bloom and Helium Filaments are resources available throughout different planets. You can exchange 50 pieces of one resource for glimmer, marks or reputation, but choose the vendor you are focusing on getting gear.

Strange coins and Motes of Light are used for buying Exotic Gear from Black Market vendor Xur, located in Tower during the weekends from Friday 9AM until Sunday 9AM.

Content above level 24

For content above level 24 you’ll need specific weapon damage. Specific damage only comes on Special and Heavy weapons, and falls into three categories: Arc, Solar and Void (blue buzz saw, yellow flame, purple swirl icons on weapons). Content above 24 often has modifiers, when in orbit after selecting your strike you can hover over these modifiers to see what they do, a common one right now is Arc Burn which means that all Arc damage from all sources does increased damage (roughly triple damage). This means that enemies with Arc damage are fairly lethal but SO ARE YOUR ARC WEAPONS! So any weapon who’s upgraded damage is over 200 and falls into one of the three damage types, save that weapon, replacing it only when you have a better one. Shield color on your enemies also corresponds to the damage that best penetrates the shield: purple for Void, blue for Arc, yellow for Solar (thanks mykkenny and BilboSwagginz @ reddit for great tips).