Shamans are pretty good at making progress within an hour, assuming you aren't trying to kill something deep within a dungeon. They are quite safe with slow, root, dots, and gate. Power-wise they are probably the second strongest solo class when you hit level 60 and get Torpor. If you have enough money for serious twinking (Fungi Tunic, Fungi Staff, JBB, Haste Item, and the best melee weapons a shaman can wield), you'll be able to level up pretty fast.
Twinked Monks do level quite fast from 1-50. With Fungi Tunic, Seahorse Belt, and IFS, I was getting like 1 level an hour on average from 30-50. It was probably faster from levels 1-29. But Monks will have less solo options as they approach 60 compared to a Shaman. Fully raid geared monks can do a lot of cool stuff, but it sounds like that isn't an option.
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