I did 1-5 wherever the starter zone was. Can make level 6-7 there easily and quickly. Don't bother with any long drop(collection) quests. Do the first one or two drop quests if they open up a bunch of other easy ones.

Assuming horde, of course.
At 5-7, I go to Tirisfal and do all of the quests there, even the drop quests except for the ribcage/skulls one and the scarlet sash one.
At 13/14ish, I move to Silverpine. Don't do any of the drop quests here except for the Dalaran Pendant one (leads to a nice staff).
At 18ish, I move to Barrens and do all the non-collection quests except for the Raptor Horns/Heads quest since it's such a fast spawn and tightly packed.
At 24ish, I go do the harpy and cenarion sons quests in Stonetalon.
I may come back and do some of the southern barrens quests here if I'm lagging behind a bit. (the silithid eggs, named mobs and gann's first quest only, though).
At 25ish or when I'm done with Stonetalon/southern barrens, I go do all of the ashenvale quests except for the Satyr horns and Warsong supplies quests (too expensive/time consuming for the length of time the loot will help you).
At 30ish, when I usually finish up the last of ashenvale, I'll move to Thousand needles and do only the purifying earth drop quest, plus the other non-drop quests.
At 33/34ish, I'll move to desolace and do those.
At 38/39, I'll move to Dustwallow, which gets me to 42ish.
At 42ish, I'll move to Feralas.
At 46ish, I'll do some of Tanaris, unless Alliance is being pricks, then I'll go to Hinterlands.
After hinterlands, usually 50-52, I'll go do Felwood, which gets me to 55ish.
At 55ish or when I finish the non-drop quests in Felwood, I'll go through the tunnel and do winterspring and back and forth to Felwood for the non-drop quests to get me to 57/58 depending on how well things went. If I'm not quite 58, I'll go do WPL for some quick XP and ding, then head to Outlands.
I'll do about 9-10 quick quests (non-drop) in Hellfire and bam, 60.