I do the kill quests and the run and pick stuff up quests - sometimes if it is just a few items I may do a collection quest but generally I skip those. It might be worth while to go to the different zones in your level range - and pick and choose the easiest and quickests quests from both e.g. do Mulgore/Durotar and Barrens/Silverpine for instance (if you are Horde - not inlcuded BC areas since I havent upgraded 3 of my accounts)

As I leveled my "normal" characters I avoided instances like the pest - I did them maybe once if at all...now I find it a fun challenge to "solo" the instances with my Shaman Army...you actually level up quite nicely if you are focused on mastering the instance and gettting phat lewt! But I am mostly 19-21 now so who knows how it will go later,