Most of the replies here are for season 26, and he’s asking for Season 25, assuming that’s not a typo.
That said, if it’s for 25, Demon Hunter is going to be the fastest for the Shadow set.
But I’d probably level to 70 as a Necro, and once at 70, complete Haedrig’s Gift as a Necro, run ubers to get a HF Amulet & Ring, and then level a Demon Hunter. The Demon Hunter can be fast to level with Lord Greenstone’s Fan, but that is kind of skill heavy. Most players really can’t level fast with it, as it requires being fairly good at massacre bonuses, while running away from high level enemies, as you will be one shot. Tag & Run is a lot easier said than pulled off.
That’s the one great thing about Cursed Chest leveling. Grasps of Essence are an 86% chance drop, and Cursed Chests force you into Massacre Bonuses, so you don’t have to worry about breaking them. They typically focus on high end difficulty (i.e. much higher than you’d normally play), with quick bursts of 100-150 which grant as much experience as trying to do 400+ bonuses that take 10+ minutes apiece on lower levels, where you have to be very skillful to pull them off.
As far as Season 26, if you have the expansion pack, there’s no reason not to start Necro, and then switch over. If Season 26 is like the PTR, the drop rate of Petrified Screams is near 90% or so, regardless of the Greater Rift Level. Hit 70 as a Necro, run 3 Normal Rifts & 3 Greater Rifts. Start the Echoing Nightmare, grab the shield, and wait out the 1 minute. It takes roughly 2-3 Echoing Nightmares to level from 1-70. The Necromancer levels 15+ minutes faster than any other class, and the above is going to take roughly 15 minutes or so. So, why bother having one class at 70, when you can have two?
Now, as far as Season 25 conquests, GR75 and GR45 solo with no sets (that means no green items. Even 1 green item will fail this) will be the fastest 2 conquests to knock out of the way. And a DH Marauder’s set will be easy for the set dungeon. The majority of time will probably just be spent leveling up gems and running a couple bounty sets to get the necessary materials to extract 20 items.
As for Season 26, the 3 gems to 65 and the GR75 solo will be the easiest 2 conquests to knock out of the way. And Haedrig’s Gift is Marauders, making everything super fast. The majority of time will just be spent running the bounty sets for extracting items.