Do a google search for "Destiny LFG." It stands for "Looking For Group" and is an okay way to find pick-up groups
of people looking to do strikes and raids.
Now, having said that, your actual mileage may vary. You can get a group of Level 32's looking for other elitists,
or you can get a group of foul mouth 12 year olds acting like elitists or you can get a decent group of raid newbies
and veterans. Again, your mileage may vary, but it's an option.
Regarding factions again... I leveled up my Cryptarch rank and got Shards and energy... leveled up Dead Orbit and got
a legendary Fusion rifle. :confused
Also, when you open a level reward from the postmaster, you gain XP. Sooo... you could just NOT
open your rewards from the faction or cryptarch until you have a bunch of them... and then basically
you'd level said faction up again... by leveling them up.

Granted you need a few of them to seed
the process,but you get a bonus for nothing.
Plus, each time you cash in bounties you ALSO level up your faction level, and you do it in
amounts of 50 or 100 points... which is faster than the 10/30 or 12/32 you get from doing patrol
missions (you get 12 or 32 after completing a nightfall strike instead of 10/30 normally). You get
30 points for an "assassination" mission (Go here and kill XXX who's doing bad things...)
compared to 10 for a regular patrol mission.
Anyway, lots of potential for leveling up a faction!