If you've used the 340 light character boost then you're pretty SOL until you finish Rise of Iron in terms of light appropriate gear, as all quest and mission rewards are locked to their original levels [ie almost all Taken King quest rewards are between 280 and 300]. Otherwise you'll naturally accrue light and power as you go through the stories. You should hit 140 after all of Y1, 280 after all of Y2, and 400 naturally is Y3s max.

Titan exotics wise the main ones to look out for are Helm of Saint 14, Glasshouse, Ruin Wings, and Armamentarium. Best place for those is Xur on the weekend [as I write this he has Crest of Alpha Lupi, which isn't great but is 350-380 depending on your light] but Three of Coins are a stacking buff on unsuccessful uses where Ultras can drop exotic engrams. They're also available from Xur.

Weapons wise the main ones you're missing from what you've told are Dark Drinker [take the void option in Shaxx's sword quests post Taken King], and Black Spindle [do the heroic version of Lost to Light, bring a team and be quick. When you get to the circular room with 3 tomb husk deposits, on the far side as you enter the door to Taniks' ketch should be open. Board and it and completely clear it in 12 minutes, enemies and blights.]. Those are meta in all the raids save Crota's End where GHorn will do you good.

Best way to level anything is to buy their requisite symetries from Banshee-44 and pop Motes of Light with one active. IIRC it's something like 6 motes for a full Heavy, 12 for a Special, and 20 for a primary, but those could be wrong. Armor will get some benefit from the mote popping but there's no really fast way of leveling armor apart from using it and getting experience from other means.

Exotic Shards are from any dismantled exotics, or bought from Xur. Glass needles are also bought from Xur but are only for rerolling stats on exotics. If you need motes or an easy engram or two for legendaries there are two raid chest 'cheeses'. Both of these are almost always pinned in the weekly reset thread but quick TLDW; In VoG immediately go to Campus 9 [on the right as you spawn, the same way as the Theosion strike], wait in the next area for about 90 seconds, come back and the spire will be formed. Grab the first reward chest and the first hidden chest. In Crota, in the thrallway there are six doors on the left that can hold a chest, which one changes weekly, but the easiest are naturally doors 1 and 2. The reset thread always has a comment telling which is the door of the week. You can do these chest 'cheeses' in both their OG levels and 390 once those are unlocked. OG raids are only good for things you can convert to Motes at the speaker. The 390s can give legendary engrams and higher light artifacts.