i don't even know what faction ranks are our how you level them up because the game utterly fails at explaining some of its systems or tying any form of narrative to draw you in. something to do with arm bands?
Yup. You need to figure out or hang around in the OT for max rewards.
Hovering the cursor over anything with text also helps.
So there are two basic factions. Vanguard and crucible. If you are rank 2 with either of them, you can buy legendary armour with either vanguard or crucible marks (as appropriate). If you are rank 3, you can buy legendary weapons. When you hit rank 3, they will give you a legendary item free.
You gain vanguard rank by doing patrol missions, vanguard playlists and the dailies / weeklies. You also get vanguard marks for playlists, public events and the dailies / weeklies. The harder the difficulty, the more you get.
You gain crucible rank by playing crucible matches. You get more if your team wins. You get crucible marks the same way.
The quickest way to rep up is by doing bounties.
There are three other factions. New Monarchy, Dead Orbit and Future War Cult. Each work in the same way. You need rep to get through the door and then you need crucible marks to buy things.
If you wear their 'mark' (via a bond or a cloak or whatever) then all rep goes to them. So potentially you could divert all crucible and vanguard rep to one of them and rep up quicker at the cost of the others.
Best thing to do is see what each of the people in the tower have and decide how you want your character to be and then go from there. My warlock is all about super super mega speed so I just have an auto rifle and everything is set around speeding up reload time and letting me spam grenades.
It's a pretty good system imo. Thing is it takes a while to 'break through' but once you start getting legendaries it just gets quicker and quicker and you end up with all the nice things. I have about 5 exotics now and maybe 9 or 10 legendaries. I've also been off work for the past three weeks though 😄
I am a complete Destiny sad sack.