To echo what some others are saying, Pet Doctor.
Once you hit 70, spend a few hours running split normal bounties. This will be the only multiplayer you need to do. You'll get keystones for opening rifts, and a good selection of quality yellows and maybe even a legendary or two. At this point, you are ready for T1 Rifts.
Run solo rifts in your yellows. Pick up everything and salvage it all. Whenever you get 500 Blood Shards, gamble with Kadala for a helm. You are looking for a Mask of Jeram. You are also looking for crafting recipes, which drop frequently. Once you get a few key recipes - Aughild's, and either Cain's or Asheara's, craft yourself some gear. You're now ready for T2.
When you get a Mask of Jeram, you are ready for T3.
If you manage to get a certain ring, The Tall Man's Finger, you are ready for T4.
If you manage to get Tasker and Theo's gloves, you are ready for T5.
Once you trick out your remaining gear with good, solid upgrades and tweak out your crafted stuff - you are ready for T6. Keep an eye out for a Thunderfury, then a Rhenho, then an SMK.