Avatar – Avatar over Deadly Calm. Deadly Calm seems great until you use it and realize the spells you would like to spam either have cooldowns or don’t even cost rage. It mainly allows you to spam Slam for 6 seconds but I usually have enough rage to spam Slam anyways. On the other hand, Avatar’s 20% increased damage is always reliable and useful at anytime.
As you're leveling, I generally recommend you just follow the natural flow of the progression through each zone. They're laid out fairly reasonably. But don't be afraid to hop around, especially if you're near a quest objective. You shouldn't actually need ALL of the zones listed to reach 62. Pick the ones you like best. It's much more important to simply be as focused as possible and flow from one quest to the next.
If you queue as a healer - take care to always have a stack of water of appropriate level. You can buy it at an innkeeper for next to nothing, but remember that it will become too low-lvl for you very fast, so you need to buy new water every 10-20 levels. Alternatively, you can buy a stack of every tier of water in Stormwind, and just always carry it with you. Another alternative, if you see a mage - always ask him (politely) to create a table for you. Grab 2-3 stacks so you have extra for the next runs.
Something to keep in mind as well is that this will make enchanting materials more valuable, since it is likely most players will now simply scrap their boe greens instead of getting them disenchanted. Also redundant dungeon/raid gear can be scrapped rather than traded to the (guild) enchanter in the run. Less stuff gets disenchanted, meaning there will be less ecnhanting materials, meaning their value will rise. All the more reason to DE rather than scrap as an ecnhanter.