I'm about to drop some glimmer on a class-specific item to start racking up reputation within a Tower faction, but I don't know what difference it'll make. Is there any difference between the factions (Future War Cult, Dead Orbit, and the New Monarchy) other than that their Tower outposts offer different items? Does joining a faction or rising in its ranks otherwise affect the gameplay? Is there any general non-cosmetic difference between the items offered in their stores?
The stats of the items for each faction has differences.
One strategy is to figure out which faction has the piece of equipment you most want and work on that faction. For example only Future War Cult and Vanguard have Hand Cannons, so if you want one of those you can decided between them.
You should also be aware that while wearing their colors you'll turn Vanguard and Crucible faction reputation rewards into the faction rewards you chose. You will not turn Crucible or Vanguard marks (the currency) into faction marks.
You can't turn Vanguard Marks into Crucible Marks. Faction items (except Vanguard) can only be purchased with Crucible marks.