as to the question, first off difficulties are called Horror, Purgatory and Doom

Horror is for CLVL 1-29, Purgatory is for CLVL 1-39, Doom can be entered by any CLVL characters but isn't recommended until you feel like managing it. However, I'm thinking about raising Purgatory restriction to clvl44, so that ppl will be forced to play Doom only after reaching clvl45. The reason for that might be that some people might just not gain enough powers by level 40 to manage Doom mode.

One thing that I'd warn against is entering higher difficulties with low age characters. There's a downside of this: even though you level faster you don't get the items powerful enough to take you further and increase your chances of getting stuck. The best way to play would be to play on Horror until level 30, then on Purgatory until level 40 or until you gain enough powerful items to protect you in final challenge.