Demo is hands down the best spec at the moment.
Please do have in mind you have to select a proper CC for your spec, which will actually play it decently. Sometimes Singular will not be enough. You should try at least a bunch of CC's and see what works best for you and familiarize yourself with the basic rotation for your class so you can easily spot when a CC is failing and tune it up, if you can.
I am currently leveling my Priest with FPSWare Priest, and after I customized the CC to actually follow the recommended leveling rotation, my Shadow Priest melts faces and has so far died like 5 times, all the way from 1-60.
Spec also matters a lot. Most specs that ship with Talented are defunct and Talented won't spend the points properly. Luckily for you, it's very easy to write your own Talented profile, so go find a leveling guide, which explains in details where you have to spend your points at every step, then arrange them in that order in your Talented Profile and you should have a working spec that will be just as efficient as if you were doing it by hand with the guide next to you. I can't stress this enough. Your spec is really important at low levels, even more important than gear. Your spec can make you or break you, so you must pay great attention to it.
Heirlooms also matter a lot. They are a bitch to grind, but once you are done, you don't need to grind anymore. Typically, Weapons and Trinkets hurt the most, as they cost 4000 Justice each, and this is a lot of Justice to grind.
Here is how it's best to do the Heirloom grind, so you will spend more time leveling and less time grinding.
+Agil gear - Druid, Hunter, Shaman, Rogue
+Str gear - Warr, DK, Pala
+Intel gear - Priest, Mage, Warlock
You can improve your grind if you are not a tank by also doing Argent Tournament dailies, and I do believe there was a profile for these somewhere on the forums.
Any gear other than that is worthless and a waste of time, as it is too niche and unsupported by HB, for example +Spirit gear is for healers, and Honorbuddy fails in dungeons, not to mention you can't really put +Spirit on a Warlock or a Mage and expect decent performance.
Trinkets - get both trinkets - Eye of the Beast and Hand of Justice and equip them both, as you can't really benefit from the same trinket in both slots. Sorry, it doesn't work that way.
Hope this helps.