See if this was pre-DLC I'd tell you to raid, do Atheon normal and get your raid gear to hit level 30 like I did. I'd also tell you to do your roc strikes to get materials to upgrade the gear. But now with the new dlc you can just buy your way to level 31 without ever raiding lol so just grind roc strikes, buy the vanguard gear, and you'll be 31 before you know it. You may still want to raid though for the shards that you will need to upgrade that gear. It's a pain to get them any other way. Edit: Rank up your vanguard to level 3 first then you can buy gear. Bounties are the fastest way, especially if you use the bounty glitch. Grind roc too to help you get there even faster.

Are you a guy?

Lvl up your vanguard or cruicble, buy vender gear, then get yourself into a crota raid

Just do bounties every day until you hit lvl 3 vanguard rank. At that point you can buy lvl 31 gear from the quartermaster

I got friends to carry my newly leveled warlock through Crota and got all my gear for 32 in two runs. That's my suggestion. Edit: checked your profile. Grind for marks so you can replace that blue gear with vanguard stuff if you can't raid

Your goal should be to reach Rank 2 in Vanguard. Once you do this you can buy legendary armor from the Vanguard Vendor. Same applies to the Crucible Vendor / Faction. [b]Note: Don't level up a faction until you reach Rank 2 Vanguard![/b] Basically do all your bounties, rank up and earn marks. Once you are able to buy the equipment do it, get a legendary body and arms before you buy a weapon. Additionally, if you have enough Strange Coins you should look to acquire an Exotic from Xur on Friday. Supposedly it's Icebreaker this week so I hope you have 17 coins! It it's not Icebreaker or Gjallarhorn you should probably get armor. If you're doing Normal Vault of Glass I encourage you to continue doing this as you'll acquire needed Ascendant Shards to upgrade your armor. Note that even though the light level on VoG gear is less than Vendor stuff it's good placeholder for the time being. Also the boots allow increased heavy ammo. You can be a 31 with 2 vendor legendaries, 1 Exotic and 1 VoG piece. Doing all of the above will get you to level 31. If you want to get 32 you need to start doing Crota's End. I encourage you to be level 30 before attempting Normal mode Crota. TL;DR - Do Roc Strikes / Crucible until max marks and Rank 2 for Vanguard / Crucible or both. Buy legendary armor (or hopefully Xur brings you an Exotic piece you could use). Acquire Ascendant Shards via VoG / Daily Heroic. Upgrade all your stuff. Then do Crota's End if you want to be 32.

Vault of glass to thirty, purchase gear from vanguard for 31. then crota.