Credit to steamer#1140 (https://www.reddit.com/user/stansteamer)
1. First, do the weekly challenge, beat it. Enter your seasonal game, claim challenge reward at level one. Huge early cash/materials boost.
2. From there I just look up a leveling guide and do rifts until 70. At some point (like once I get a legendary worth cubing) I'll go snag the cube and do a round of bounties as that's one of the first things required by the season journey.
3. Once you hit 70 it should take you like 20 minutes to get the first Haedrig's Gift, tops. Look up a 2-piece build and roll with it. 4 piece should be quick and easy as well, and usually a big power bump. Getting the last two is the hardest as you'll have to beat a GR20 solo. This is still generally not difficult.
4. Once you've got your set find a 6-pc starter build and start running rifts for keys. If you die your difficulty is set too high. If it's taking longer than ten minutes - too high. Look up which gems the most popular builds for your class use and work on levelling them all, or at least the ones you may try, up to 25.
5. Run another round or two of bounties to get all your gem recipes.
6. Use Kadala for armor pieces.
Upgrade rare weapons to get the ones you need.
Pray to the RNG gods for good jewelry to drop.
Look up a complete build you want to aim for and start working toward it. Wardrobe your starter build in case you don't have enough pieces to make the complete build effective yet.
Alternate between rifts and greater rifts while you level legendary gems and farm regular ones. You want to power creep until you can solo a GR70 at which point primal ancients unlock to drop. In fact I believe this season, one automatically drops upon beating the GR70 boss.
Leveling tips for Seasons