Going over gr30 should not be a problem on any class, so pick the one you would enjoy the most.
This late in the season, if you're not gonna get powerlevelled, I would suggest levelling up in bounties on low level, skipping as many mobs as possible to get riftkeys. While this is not the fastest way to level, you get plenty of keys.
Keep all lvl70 survivability items, even shield. Join public T6 rifts with your keys, and loot. There will always be a WW barb running way faster than you killing most of the mobs, they wont even notice you're not doing any damage. You'll have your sets (and trial keys) in no time.
From here, you can level you gems. You probably will have to do it solo, since people do inspect for grifts. But again, if you aim for 30, it shouldn't take more than 20 hours after hitting lvl70 this way
Good luck and enjoy.