To begin, take First Aid and max out your abilities in that profession at the earliest opportunities. When healing others with bandages you should always use the highest rank bandage it's possible for a character of your level to produce. There are two reasons for this. First is the "Recently Bandaged" debuff. If the bandaging should be interrupted, you want to have accomplished as much healing as possible in the time you were able to bandage. Second, healing others quicker means you're able to heal your next target sooner.
As a rule, never, ever apply a bandage to a target that has aggro. As soon as that target takes his next hit, the bandaging will be interrupted and he'll have received the "Recently Bandaged" debuff for naught. Instead, work with your group to establish aggro sharing so you can work a bandage rotation on your tanks, or look for items with a "Heals your Target" effect. Draenei can also use their Gift of the Naaru as a heal spell in this case.
Also, do not neglect Anti-Venoms as a component of first aid. The most effective healers decurse as well as heal. If you want to do your best as a healer, Anti-Venoms are essential.
The type of items you'll be looking to carry are those that give you healing abilities or otherwise impact group stats in a positive way. I found these to be of interest. There are almost certainly other items I've missed. Among these are the sort of items you'll be using to heal a target that has aggro.
HeadSome character choices complement the un-healer concept better than others. Only Engineers, for example, can use Jumper Cables and Recombobulators. Mages can naturally decurse, as well as provide food during fights. Warlocks can provide healthstones. But both mages and warlocks are limited to cloth armor, meaning there are a couple items on the above list that are inaccessible to them. A hunter who feigns death may be able to recover a party using his jumper cables on the rezzer. And as mentioned before, any Draenei receives the delicious Gift of the Naaru.
-  Admiral's Hat
-  Pendant of the Agate Shield
-  Citrine Pendant of Golden Healing
-  Aquamarine Pendant of the Warrior
-  Embrace of the Dawn
-  Living Ruby Pendant
-  Thick Felsteel Necklace
-  Gauntlets of the Sea
-  Ankh of Life
-  Minor Recombobulator (140 eng.)
-  Goblin Jumper Cables (165 eng.)
-  Major Recombobulator (275 eng.)
-  Goblin Jumper Cables XL (265 eng.)
-  Black Husk Shield
-  Everglow Lantern
There are some good tools available to help manage your healing. I prefer Clique and Grid. With Grid, I can see who has aggro to avoid bandaging them, who has a debuff on them that I can cleanse, and who has an incoming heal (meaning they don't need to get bandaged). The Grid squares that provide all this data support click-casting, and Clique is the tool I use to do that. I configure Clique to use the healing items and bandages I have on me when I click a player's Grid square, and from there healing is as simple as paying attention and clicking the squares to use the right item on the right person. A comprehensive discussion of Clique and Grid is certainly beyond the scope of this missive, but suffice to say they're extremely powerful tools when wielded competently.
Remember also to maintain your cooking! Having stacks of buff foods to hand out to the party helps to lessen damage taken and improve damage done.
Can all this make you into an effective main healer? No. Not a chance. As an off-healer, though, I think it's feasible. Back to the idea of the melee hunter -- which seems more useful to a group: an off-healer with party buffs, or a really poor melee fighter? It's something to think about.