How does one most effectively progress from Torment I upwards?

I'm wondering what are the mechanics involved in being able to handle higher difficulty levels once you have a character at level 70. I tend to do bounties and rifts and I up my paragon levels and slowly I seem to be able to cope better at my current torment level so I go to the next one, but I don't really understand specifically what it is I'm doing that is making the current level easier.

Obviously the buffs provided by paragon points help to an extent, as does the cube powers, and finding and equipping better gear. I suppose mostly I'm wondering about the better gear drops. Is the quality of gear that drops related to the Torment level I'm playing at? Is it, along with probability/randomness, going to be some function of the level of my current equipped gear, or my paragon level?

With regard to set items, gear that I have at Torment I is not going to suffice if I try to step up to Torment IV. Should I be looking to craft a new version of a set item to replace it? And if so, what aspects of the game will determine that the newly crafted version will be better than my current version? Is it purely random?

tl;dr: how do I give myself a better chance of ensuring my gear levels with me in the end-game?

If you keep doing what you're doing right now, you're on the right path. Remember that it takes some time and luck to make a character strong.

To answer your question about quality and frequency of drops in difficulties:

• There are some torment-only legendaries that will only drop from torment 1 and above
• Each torment level increases the chance of getting a legendary. The quality of the legendaries will only be affected indirectly. Since more legendaries drop you will also get more ancient legendaries which are a lot stronger but also more "bad" legendaries.
• Crafted legendaries can proc as ancient ones but it's very rare and costs a lot of resources. Most legendaries have partly fixed and partly random stats. These rolls are not affected by difficulty. (The resource drops in order to craft them are though)
• Gambled items also have a chance to be legendary but the chance doesn't increase with difficulty. Stats and items are completely random although the type of the legendary is restricted.
• Some enemies like greater rift bosses and certain treasure goblins have an increased legendary drop chance.

Your main goal should be grinding for legendaries and/or sets (usually luck based) in order to boost your damage and defense but there are some tricks you can do gain a good boost in dmg/toughness that aren't too luck based. Personally I wouldn not recommend crafting unless you're getting really unlucky since it costs too many resources you could otherwise spend on reforging your gear.

Seasonal Journey

Now if you're playing a seasonal character you can complete your season journey in order to get a "free" set which helps a lot (note that you will get a set only once per season).

Most sets you get from the journey are built like this:

• 2pc bonus: Usually a mediocre damage upgrade that allows you to rush through torment 1-2
• 4pc bonus: A strong defensive boost that helps with surviving on torment 2-6. At this point torment 3 and/or 4 are your preferred difficulties since your damage isn't really good enough for 5-6.
• 6pc bonus: This is a huge damage boost in most cases. We're talking about 1000-5000% more dmg than before. With this damage you can start grinding Torment 6-7.

After this your main upgrades will come from finding (specific) ancient legendary Items and upgrading your legendary gems.

Gems

Gems are also a great Way to increase your damage. Having a high level green gem in your weapon will boost your damage by a ton. It's really easy to farm specific gems with the Broken Crown which is a fairly common item. Especially if you have access to the greed portal. Your main-stat gems in normal armor will give you a good boost but you should always prioritize getting the 130% more crit dmg on your weaponslot.

Non seasonal characters / alts

If you don't play on a seasonal character or you've already completed the seasonal journey all you can really do is grind, grind, grind. The things I've mentioned above should help you getting your legendaries faster but you won't be able to progress as fast as with a "free" set.

While not a full answer to your question, I feel this is worth adding:

One of the best places to farm legendary items is in Greed's Realm, as Jutschge mentioned. This also gives you plenty of gold, which you will need for enchanting to optimize your builds. This Realm can be easily accessed by breaking down Puzzle Rings in Kanai's cube, allowing you a one time entrance to the Realm per ring. Plenty of treasure goblins are inside, and if you can kill them before they escape, you've got a good chance of them dropping a legendary or two. The final boss spawns treasure fiends as well, so it's wise to kill as many as you desire before killing Greed to get even more loot. Greed gives a legendary gem, as well as a fantastic amount of loot, further increasing your chances for legendary items.