Using Healing Gear To Burn Sunwell Daily Mobs
I found my best results came from just wearing my ordinary healing setup, if only because it vastly outclasses my Elemental set. I have about 1490 or so bonus healing and roughly 650 spell damage on my healing set, while my Elemental set has around 800 spell damage on it. If your Elemental set is better than you may want to use it instead, but from my perspective the extra damage from that 100 more spell damage was completely unimportant compared to how much less my self heals ticked for, not to mention how much less oomph my Earth Shield had.
In my healing setup, I would put either Frostbrand or Flametongue weapon on my healing mace (a Hand of Eternity, since Karazhan hates me) and make liberal use of Earth Shield for the healing and the fact that it prevents caster interruption to a degree. With this set-up and the proper use of Grounding and Searing Totem, I could do the quests Don't Stop Now and Disrupt the Greengill Coast with relative ease. I found it to be easier to kill the melee male Naga mobs because the casters have an annoying Silence and can cast that Frostbolt spell of theirs over and over again, meaning that even with a Grounding Totem and Earth Shock some of them got through, but between proper totem placement and keeping Earth Shield up as much as possible, they still went down pretty easily.
Taking on Caster Mobs
The demons and Blood Elves you have to kill for the quests The Battle Must Go On and Crush the Dawnblade are a little harder, but still doable. For starters, since I don't like giving up my Earth Shock for the caster mobs, I tended to pull them using Nature's Swiftness and a Lightning Bolt or Chain Lightning on the warlock/imp pulls. Against these mobs, Grounding Totem is an absolute boon, chewing up some of that imp's fireballs while you unload Earth Shocks on the warlock and take advantage of your Earth Shield to keep you healed and able to cast Chain Lightning whenever it's up. It's even better against the caster demons. Against the melee demons, just pull them with the biggest damage spell you can, Frost Shock them as they run in, try and get another big damage Lightning Bolt off before they arrive, and then use shocks and the Earth Shield's benefit to Lightning Bolt them in-between Frostbrand or Flametongue weapon on your melee.
This method will pretty much work for any soloing or grinding you need to do. Back before they changed healing gear, I wouldn't have recommended it: in fact, I had to get over my ingrained bias against healing gear and really force myself to try it out to see that yes, for my level of gear, it makes more sense now to roll in my healing kit than it does to have all that Enhancement mail in my bags, taking up space. Still, if you absolutely have to roll into the thick of things and fight it out, here are some things to keep in mind.
Working that Two Hander
Always switch back to healer gear when you're about to put Earth Shield on yourself. Sure, the nerf to charges on ES makes this less effective than it used to be, but it's still better to cast it on yourself with 1400+ healing than it would be with barely 600. Since you'll be counting on Windfury, get the biggest, slowest 2h weapon you can find: I have Legacy because our hunters already had it. Quite honestly, I wish it was slower. But since you don't have Stormstrike to take advantage of and you're not concerned about the Windfury cooldown, it's not as major a deal for you. If your mana seems to hold up (mine didn't) you can drop Strength of Earth and Grace of Air to boost your melee attack power and crit chance but don't lose sight of Grounding Totem's utility against caster mobs. If you happen to have very solid Enhancement gear (perhaps you PvP on weekends as enhancement, I don't know, you could be a masochist) you may want to use one of your weapons and a shield instead of a 2h for added survivability. Vanir's Right First of Brutality is only 11 dps less than Legacy, after all. Likewise, if you have a really smashing set of Elemental gear you may prefer the raw damage you can pump out in it to the higher survivability of your Resto gear.
Elementals Are Your Friends
However, it's fair to say that you don't need to swap sets to solo or farm or grind quest mobs anymore. While it's still true that you can't heal a mob to death, you can certainly heal yourself while simultaneously burning or freezing them to death. And please, don't forget your elementals! You can use one of each every twenty minutes, so if things get dicey drop one. If you use Fire Elemental totem, in two minutes you can drop Earth Elemental, so don't be too stingy with them. These totems exist for emergencies, so if you've been happily grinding away and suddenly realize that everything has respawned around you and you're in the thick of hostile mobs, that qualifies. Also don't be afraid to use Heroism, even though it is much more effective for melee types: faster lightning bolts and a few lucky Frostbrand or Flametongue procs on a faster melee swing could help out quite a bit if death is on the line. Sure, you can Ankh, but you don't want to, save that for instances.
Okay, that's enough: experienced Resto shamans already know all of this, and it's a good starting place for people just hitting their stride. Admittedly, it's biased towards level 70: I just don't happen to have access to a Resto shaman of lower level at the moment.
Next week, I have no idea. Not turkey, though. We covered that already.