I got an untwinked warrior to 30, 100% solo in 2 weeks on green without going overboard on time investment.
Hybrids can not be the fastest due to the hybrid exp penalty, until velious.
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edit: I did not see the solo part...
If you're not anti-social and can get a decent pierce weapon, Rogue.
Halfling Rogue is a fantastic raid character. Hopefully guilds start PLing some of them to use as guild alts.
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Halfling Rogue requires 85.45% exp