I think the fastest from 1-99 is construction, even using conventional methods. It takes less than an hour to be able to make Oak Larders, and then with mousekeys you can get 500k xp/hr. Then with Mahogany Tables and mousekeys you can get 800k xp/hr. This method will get 1-99 in about 16 hours total, less if you do the mousekeys to get more than one thing done per tick. 800k xp/hr is very fast, and the level requirement of 52 to make Maho Tables is extremely low--most other skills don't see good rates until they are nearly level 90+.
EDIT: Crafting might also be just as fast, if not faster. Gem cutting is very fast exp. Even cutting sapphires is 200k xp/hr (extremely fast grinding until you can cut ruby and higher), and cutting dstones is around 1m xp/hr.
