I should also add you need to make sure you join a faction as well - either Future War Cult (in a small room above the hangar area), Dead Orbit (in the hangar area, near the Vanguard weapon vendor/ship mechanic) or New Monarchy (near the speaker, you go to the left when you come into that area). You earn reputation with your faction when you earn Vanguard/Crucible marks and you can also speed it up by donating items to your faction (such as motes of light, heavy ammo synths etc.) to speed it up. Ranks 1 and 2 let you buy specific faction armour and rank 3 lets you buy specific faction guns plus each time you rank up you may get a legendary item from your faction.
You should have chosen one when you started Taken King as I think you have to go to each one as part of the introductory quest but thought it worth mentioning in case you haven't. Dead Orbit is currently a popular first choice as their rank 3 Scout rifle Hung Jury is one of the best in the game, it comes with Firefly and Triple Tap which means precision kills on enemies cause them to blow up and weaken those near them and the Triple Tap means rapid precision hits give you more bullets back in the magazine. That gives it tremendously flexibility as it can quickly clear out low level enemies by blowing them up and it's also good for stronger enemies as repeatedly getting precision shots means you'll get ammo back allowing for much longer shooting sprees before needing to reload.