If you don’t care about leaderboards - play what you want!
Play a Hammer of the Ancients Build with the Immortal King’s set - it has skills that allow quick movement and it is powerful as well. I used it to level up my Barbarian this season before I switched to Whirlwind.
Go to the barb forum and you’ll find a truckload of build options with details on builds, gear, skills and more.
But also - many classes have a build that’s fast and powerful (tho maybe not as much as WW) … you aren’t limited to Barbarian.
and also - go to https://d3resource.com/difficulties/ and you can see the nitty gritty for each level like how many materials you get, how many legendaries might drop from the RG, gold and XP bonuses, and even monster health/damage scaling.
Hammer of the Ancients and Seismic Slam can work if you have the supporting legendaries.
HotA needs Gavel of Judgement and Bracers of the First Men.
SS needs Fury of the Vanished Peak and Bracers of Destruction.
Note: HotA can be used to move and will not activate until an enemy is within range. Slam activates on every press and you need to get into position to use it effectively, but has a longer range.
personally, the WW Barb is my favorite set. I also like the new Ninety Savages Set with Frenzy but it is rather fragile outside high density mobs. The Furious Charge Build can also be fun. You can do a good Furious Charge or Frenzy build using Legacy of Dreams. However, if you want to run higher GRs as a Barb, you are going to pretty much have to use one of the top set builds. Getting to the point where you have all of the pieces of those sets usually requires an LOD build using the skill that where you have the most legendry pieces that boost that skill regardless of which skill that is. A lot of LOD builds will get you up to T10 where the Drop rate on mats, legendry items and set items are more favorable and where you can significantly boost the levels of your legendry gems. After you get sets put together, you can run higher T levels and GRs. Remember Grs give you a lot more experience growth than Bounties and NRs at equivalent Torment levels.