The short version of my casting order and some fury tips. I'm not even a raiding fury anymore, but this should give you a place to start:
you want to keep the following spells down at all times. mash them as soon as they repop, in basically this priority order (in other words, if Typhoon and Ball Lightning are both castable, cast Typhoon first):
Typhoon
Lightning Bolt
Death Swarm
Starshower (only if 2 or more mobs in group)
Ball Lightning (if blue AEs are not a problem)
Sunrise (only if 2 or more mobs in vicinity and blue AEs not a problem)
in between these, you want to cycle through the following for infusion procs, again in basically this priority order:
Hibernate
Fae Immolation (only if you have 5 points in the AA to increase cast speed)
Recovery of the Untamed (level 14 group heal) (or Untamed Regeneration depending on if you need the extra heals in group for choker wearers, etc)
Pact of the Cheetah
Abolishment (only if not needed for cures, I generally hold this one back)
Furies are rediculously power inefficient, so you'll want to have almost a full set of gear that decreases power cost or procs self power and use as much of that as is necessary to regen power.
You'll also want basically a full set of +dmgcrit and +dmg gear, as well as a full set of +healcrit and +heal gear, and use them situationally. Some fights there is absolutely no need to wear your dmg gear (Leviathan, Venril Sathir) so have something in your bags worth putting on in those situations. In groups I usually use the power set assuming I'm with a decent group that's pulling quickly, while in raids I'll use either the dmg set or heal set depending on where we go and what we're killing. It doesn't take much time to swap in the heal set for named mobs after going through the trash in the dmg set.
That said, don't run yourself out of power for dps, ever. Heals are still your top priority.
Keep your eye on the main tank for single target heals (Grand Elixir and Dire Salve ONLY, our heal over time is worse than the Warden's one, and will overwrite that better heal while at the same time wasting both your power and the Warden's). The vast majority of the time, however, your job is to simply keep your group alive and do the most dps possible while fulfilling that duty. Chances are you'll be in the caster group, with caster buffs... use them.