What is the best way to upgrade gear in Diablo 3?
Here is my typical priority while starting a new season (similar to starting out completely new):
- Fill every slot with a legendary. To do this, I will gamble using blood shards on every slot that doesn't have a legendary in it (other than weapon, I craft those). Once you have a complete set of legendary gear, no matter how bad, you can handle torment 1 no problem.
- Complete a class set. Any complete set, even the worst set, is drastically better than having no sets at all. Pick the set you are closest to completing after doing step #1. If you are on seasons, completing season journey chapter 2-4 will give you a free set.
- Complete the other items required for the class set (jewelry, weapons, etc). I typically use the kanai's cube to upgrade rare weapons into legendaries for the specific one I need. Also, completing the focus and restraint ring set is usually a huge damage boost.
- Collect some Legendary gems. Even level 1 gems can be a huge boost in damage if you pick the right ones (bane of trapped, zei's vengeance, bane of powerful, etc).
- Start farming for the best set of my class. I use blood shards to gamble for armor pieces, and kanai's cube to upgrade weapons for the one I need.
- Once you are using your class's best set and have the right legendary gear in every slot, you should be easily T10 capable at this point. After this, its the long grind of slowly getting better mods on your gear and pushing your way up to T13 and high GRs, upgrading gems, etc.
Upgrade gear is not a very good term to use in Diablo. Gear upgrades could have multiple meanings. Are you trying to upgrade it by getting a set, just stat upgrades or a specific item? All of these would be valid for "upgrading gear".
I would first suggest pinpointing what kind of upgrades you want to get. You should first aim at a specific build that you want, and then looking for that.
As for your question, here we go:
Crafting recipes in Diablo are generally useless unless you have really weak gear in a specific slot. I'd stay away from them because you can use salvaged parts in the cube.
Bounties are good for cube materials, which will ultimately help your build, but not your standard gear items.
Blood shards are great, but stay away from weapons and jewelry. They are too expensive and are not cost efficient while first upgrading your gear for the late game.
There are no specific bosses that are better for gear and bosses are not worth it.
When you are looking for a SPECIFIC piece of gear, the fastest way to obtain it is to turn a rare (yellow) item into a legendary of that type through the cube. You can view the cube recipe's by clicking the little book icon in the cube menu.
The best place to upgrade gear is rifts because there is a bonus to legendary drop rates. You should always go to a higher difficulty if your clear speed will remain high. Always go down a level if your clear speed drops to something that is not time efficient.