Those are very relevant questions, as the efficiency of the process depends greatly on how easy it is to obtain the item.
Keep in mind that affixes and ascended bonuses share the reroll counter!
So if you affix-reroll a lot first, then ascended-reroll is expensive later, and vice-versa.
Usually, you want to start by rerolling the Ascended bonus until you get it right, and only afterwards reroll affixes. This is because Ashes are much easier to get than Soul Fragments. But sometimes you have to do the opposite.
More Details…
Easy items to obtain:
Item type: MIs that are easy to farm, and drop in large quantities in certain area
Most efficient strat:
- Farm a lot of MIs, and keep all of those that are single-rare.
- The suffixes dropped don’t matter. If you get a double-rare or the one suffix you want, that’s great! But be prepared to throw those items away because nothing guarantees that they will roll the ascended bonus you want.
- Ascend one MI at the Kurnhold NPC. Then, go to the inventor and reroll the Ascended bonus while the cost of rerolling = 1 Soul Fragment. This guarantees the average cost per attempts is the lowest
(The lowest average of Souls per reroll is 1.75 at the 8th attempt, going for a cost of 2 per reroll is above the average and not worthwhile. First Ascend cost is 7 and not 5 to account for other costs such as Aspects of Beronath etc)
- If you reroll enough that the cost to reroll is now = 2, sell the item, and start again with another one of the MIs that you farmed.
- Repeat the 2 steps above until one of the MIs gets the Ascended bonus you need. Then use as many Ashes as necessary to reroll the prefix and suffix to the double-rare you want, and voilá!
If you can survive the ordeal, you can put 5 Soul Fragments on the Altar before you go farming, and then some of the MIs that drop are already Ascended. It doesn’t matter which Ascension bonus they got; you can reroll those items immediately with a cost of 1 Fragment only, instead of paying the initial 7 in materials. Should save you a lot of Fragments and materials overall.
Hard items to obtain:
Item type: Legendaries with low drop rates or Conduits that need many crafting attempts at the blacksmith to get the right affixes on.
Most efficient strat:
- Just reroll the Ascended bonus as far as you need. At a certain point each reroll might cost you 5 or 6 Souls, which is very expensive. But there’s no other choice. You only have 1 copy of your item anyway, and you can’t sell it to try again
- In the rare event you farm a 2nd copy of your item, then Ascend the 2nd copy and reroll that one while it has few attempts and is cheaper than the 1st copy you got.
“Medium” items to obtain:
The middle ground between the 2 extremes presented above is: you have an item that drops sometimes, but the drop rate is not crazy. It’s not the rarest MI in the game, but getting more than 5 copies per hour of farming is a stretch of luck.
In this case, keep every single copy of the item that drops, even if not single-rare. You should still reroll the ascended bonus first. However, when rerolling, it’s OK if you pay 2 Soul Fragments or even 3 per attempt. I recommend that you never sell these items even if they reach a cost of 4; keep them in your stash just in case. If you end up farming a lot of Soul Fragments but not a lot of copies of your items, the specific economic situation that your character is on might allow you to pay 4 Fragments each, or more.
Rerolling Seeds (basic):
This is the last thing you do, to min-max the last few drops of power into your character, when you already have the item with the correct prefix, correct suffix, correct BS bonus (if applicable), and correct ascension bonus. Choose 1 or 2 of the most important stats on the item. Usually these have small ranges, like “3-5% Phys res”, or “7-9% Attack Speed”. Then, reroll the seed until both of those are maxed, and stop there. You can’t keep going because things get expensive and you might run out of materials mid-rerolls, and you end up with a worse item seed than you started. If you want more than 2 stats “perfected”, than you need another strategy:
Rerolling Seeds (to perfection):
To really get many of the stats on your items close to a perfect roll, you will need a LOT of materials, and attempts. If you already rerolled the basic, nothing guarantees that, if you reroll more, you will end up with a better result. You may actually lose stats on your item if you’re unlucky.
Thankfully, there’s a strategy around this problem too:
- Have 2 copies of every BIS item on your character.
Yes, this includes prefixes, suffixes, bs bonus, ascended bonus, components, augments, everything. With 2 copies you can, safely, wear the 1 item with the best stats, and keep the 2nd item in your stash to reroll. After a big farming session, if you have a lot of ashes, take the 2nd item to the inventor. Now you’re rerolling a spare, so you can guarantee you won’t “brick” the item you have equipped. If you get lucky with a better seed on your spare, swap the 2 items, and repeat the process safely as many times as you want.
Dangers Of Magic Affixes:
If a BIS item is 1 rare prefix and 1 magic suffix, then the order of operations should be: 1) reroll the magix suffix, 2) reroll the ascended bonus, 3) reroll the rare prefix. This is because step 1 can fail, and once the suffix is rare it’s impossible to reroll it back to magic.
This is a particular nightmare if you’re doing a yellow-only item challenge. Rerolling affixes often turns your item green, and then it’s bricked. So in this case you have to do the opposite: get (or craft) the base item you want with the right BS bonus you want, and at least one of the affixes. FIRST reroll the other affix until you get both affixes right, and only later try Ascending the item. If you do it the other way, you might have to sell an Ascended item because it became green and now it’s unrecoverable trash.
It helps if you check Grim Tools to see which is the “most unlikely affix”; in other words, the one with the biggest number.
You want that affix to come out of the blacksmith directly, and reroll the one with the smaller number.
Good luck and happy rerolling 
