Leveling quickly at the start of a new season can save you a lot of time. Ever since Challenge Rifts were introduced, this process got sped up significantly as you are able to gain a good bunch of materials right off the bat. This includes: 15x All Bounty Materials, 35x Death's Breaths, 475x Blood Shards, ~365x Reusable Parts, ~350x Arcane Dust, ~125x Veiled Crystals as well as 5.1m Gold.
With these materials at hand, you can immediately level the Blacksmith and Mystic to max. and start gambling at Kadala at level 1. Additionally, you can craft a yellow level 70 weapon and upgrade it to legendary in the Kanai's Cube to have a chance to gain a big power boost. Depending on your class and leveling strategy (more info here), this can easily allow you to jump multiple difficulty settings and reach 70 much faster than otherwise possible. Some classes have it easier than others, especially Necromancers, Barbarians and Demon Hunters. Other classes can also build very strong combos but usually require a bit of luck to do so.
Using the Materials
Crafting Once you unlocked the cube, go to the Blacksmith and craft one class-specific weapon that you will try to upgrade into an useful option with the Upgrade Rare feature (3rd cube recipe). You only get one attempt as you are limited by Death's Breaths and it comes down to luck, so you better hit something good! The chances are between 17%-100% to get one of the top choices depending on your class. Some of them have decent alternatives that are helpful even when you don’t get the best one and can easily jump a few difficulty levels. By getting the right item here you can easily save up to half an hour or more on your journey to 70.
Gambling With your Blood Shards, you want to gamble early on at Kadala (gamble table here) to try and get an item with a big multiplier (that ideally synergizes with your weapon). Typical gambling choices are Gloves, Bracers, Offhands, in some cases you also want to wait until a certain level or change what you are going for depending on your crafts or other gambled pieces. At level 1, the pool of possible items is rather small, which you can use to your advantage to almost guarantee a good result that can carry you all the way to 70. In some cases, better options unlock a little bit later so you should hold onto your shards until exactly the mentioned level. The chance to get any legendary at all from gambling 475 Blood Shards (19 attempts) on armor pieces is 86.5%. The chances mentioned on specific items below are the outcome in case the gambled piece is a legendary.
A generally useful option that is available to all classes is Pox Faulds that can already provide a great boost during the early levels. They are not really the best option for any class but deliver consistently good results instead.
Crafting Possible outcomes from two-handed Mighty Weapons (4/6 are good results):
Blade of the Tribes
Fury of the Vanished Peak
The Gavel of Judgment
Barbs have good chances for some really big damage here. Two of these weapons can even be combined with easy level 1 gambling results Hammer of the Ancients or Seismic Slam, both of which work great with the combo.
Gambling Bracers (lvl 1) yield very strong results early on with Bracers of Destruction and Bracers of the First Men both offering great multipliers that could even synergize with your crafted weapon (both 50% chance). Even on their own you can do reasonable well with just the gambled items. Alternatively, rings could give you Band of Might (50% chance), which will make your life a lot easier.
Crusader (Craft Flails, Gamble Bracers/Shields)
Crusader has the option to go either one-handed or two-handed Flails, slightly favoring the former. The good part about Crusader is that it's quite easy to build a synergy between the crafted and the gambled items should you manage to hit something.
Crafting Possible outcomes from two-handed Flails (3/8 are good results):
Fate of the Fell
Possible outcomes from one-handed Flails (3/7 are good results):
Gambling Bracers or Shields(lvl 1) are useful and it depends on your craft what you will go for. Denial (50% chance) is great for Sweep Attack after getting Golden Flense, but should be gambled regardless in case you got nothing from your craft. Gabriel's Vambraces (100% chance) or Guard of Johanna (50% chance) can enable Blessed Hammer especially after upgrading into Johanna's Argument before. At level 23, Akkhan's Manacles becomes available for Blessed Shield (50% chance). If you got a Fate of the Fell, you can gamble for Bracer of Fury at exactlylevel 33 (33% chance).
Crafting Possible outcomes (2/2 are good results):
Lord Greenstone’s Fan
Demon Hunters are blessed here: They are guaranteed to get something good, but still fall behind the other classes in terms of maximum potential. Even if you hit the best case scenario with Lord Greenstone’s Fan or Karlei's Point and then gamble a Holy Point Shot at level 31, you will not perform as well as a lucky Necromancer or Witch Doctor. Regardless, your leveling experience will always be at least solid no matter what.
Gambling Compared to how well the crafting goes, Demon Hunters are not lucky when it comes to the gambling options. The main options here are Bracers (lvl 1) for Wraps of Clarity (100% chance), Helms (lvl 1) for Leoric’s Crown (100% chance) or Quivers at level 31 for Holy Point Shot (25% chance), especially if you upgraded into Karlei's Point. Impale with both items is extremely strong and will allow smooth sailing all the way to level 70 even up to Torment 6 difficulty. In case you are going with Fan of Knives, the most efficient strategy is to go for big massacre bonuses on higher Torment difficulties when in solo or just use it to oneshot elites for your party in groups. In this case, if you are feeling really lucky, you can try to go for The Ninth Cirri Satchelat level 34 (14.3% chance) to allow some trashkilling while waiting for Lord Greenstone's Fan to recharge.
Monk (Craft Daibos, Gamble Bracers/Boots)
Crafting Possible outcomes from Daibos (4/8 are good results):
Incense Torch of the Grand Temple
The Flow of Eternity
Monks are not really great here. The top results all work pretty well and potentially synergize with easy gambling results (Incense Torch of the Grand Temple + Pinto's Pride or Balance + Cesar's Memento), but outside of that the class doesn't offer very much when compared to the top dogs. If you don't get anything, you should either play support in groups or focus on Exploding Palm. The only other two outcomes that do something are The Flow of Eternity and Flying Dragon, both of which are not really great though.
Gambling Bracers (lvl 1) have a guaranteed decent to good result with Gungdo Gear, Cesar's Memento and Pinto's Pride and you will most likely get a combo here if you manage to hit the craft. Aside from Exploding Palm, none of these skills will really make a dent when they are not combined with the respective weapons. The alternative here is Boots (lvl 1), where you can get Rivera Dancers and The Crudest Boots. The Mystic Ally bonus can carry you on its own and if you happen to get them early, you could save some shards for lvl 17 to try for Bindings of the Lesser Gods.
Crafting Possible outcomes from two-handed Scythes (2/4 are strong results, 2/4 are decent results):
Maltorius' Petrified Spike
Nayr's Black Death
Necromancers have by far the best start of any class in the game, even when they get unlucky. Their base skill damage is generally high on some core skills (e.g. Corpse Explosion) and they have access to a variety of solid options from both gambling and cubing at level 1. Bloodtide Blade enables Death Nova and Reilena's Shadowhook buffs all builds by a decent amount and is especially useful for resource-hungry builds such as Skeletal Mage. Even Maltorius' Petrified Spike is useful as an initial nuke to produce corpses for Corpse Explosion.
Gambling Gloves (lvl 1) gambling will almost guarantee you a great outcome with Grasps of Essence (100% chance), which will buff your Corpse Explosion to remarkable levels should all else fail. Rings (lvl 1) for Circle of Nailuj's Evol is another great option especially if you upgraded into Reilena's Shadowhook. If you get super lucky, you could even try to go for Razeth's Volitionat level 19 after acquiring the ring before.
Witch Doctor (Craft Spears or Ceremonial Knives, Gamble Mojos)
Crafting Possible outcome from Spears (1/2 is a good result):
Possible outcomes from Ceremonial Knives (2/12 are good results):
The Dagger of Darts
Witch Doctors don't have it easy here. The only really great option here is The Barber, which can be combined with Gazing Demise with a very high chance should you get it. In that case you can get extremely lucky and make leveling to 70 a breeze with Spirit Barrage. A safer option is to go for Scrimshaw buffing Zombie Charger, which gives you a great boost as well and has a pretty high chance to roll.
Gambling Mojos (lvl 1) for Gazing Demise (100% chance), especially if you upgraded into The Barber. The other option are Helms at level 34, where you can get Carnevil or Mask of Jeram (both 12.5% chance), which would go well with The Dagger of Darts, but the odds are not in your favor.
Wizard (Craft Wands, Gamble Sources)
Crafting Possible outcomes from Wands (4/10 are good results):
Fragment of Destiny
Wand of Woh
Wizards are generally quite bad for leveling, even with one of the good outcomes. The only really good option is Hydra with synergizing items. The big issue is that despite these items having a decent multiplier, the chances to achieve a combo are not great and for the rest there is nothing to combine them with from Kadala. Should all else fail, try to play around whatever you managed to get.
Gambling Sources (lvl 1) for Winter Flurry (100% chance, especially good if you managed to craft a Serpent's Sparker) or at exactly level 33for Etched Sigil (50% chance). Make sure you don't overlevel, as at level 34 three more useless offhands become available. If you are feeling super lucky after getting an early Winter Flurry, you can also try to go for The Magistrate at level 34 (11% chance).
First thing in a new season, finish the challenge rift to obtain the necessary materials.
Acquire the Kanai's Cube before you level too high.
Craft and upgrade a class-specific weapon at level 1 to try to get a big damage multiplier.
Gamble the right armor pieces at the right levels, adjust for what you crafted/gambled.
Use what you get the best you can, even if the results are unfavorable.