Vanguard Tiger level strikes for +6 marks a time.
Bounties for vanguard rep.
Farming public events with Beacons in between.
I'd actually consider going level 2 vanguard, then level 2 faction of your choice, THEN taking the one that has the weapon you want to level 3.
Reason being you need gear to level, and you only get 100 marks a week. You can use crucible marks for faction vendors so you can, if you have time of course, get two pieces of legendary armour in a single week: one vanguard and one faction.
It depends though, I got lucky with a couple of legendary primary weapons, you might be finding you want one of those more. I think armour is more useful at first though, opens more content.