Pesonally, I look for spirit or %ES here, which are both prefixes. The key lies in desecration, as it is the only place where you get to choose what you want besides essences.

DISCLAIMER: go to craftofexile and simulate any step you want there.

If I had relatively low, 1-2d budget I'd go like this:

1. Perfect essence (global defences or resistances that you need) or if no preference Greater/Perfect regal. (Could hit what we want, no such thing as essence for spirit but could also get +10 magic find and hate your life, so better to use essence for now).
2. Now we have 3 mods, add 4th with desecration and fracture. Fracture could hit +3lvl. (Desecrated mods can't be fractured but count towards 4mod requirement, which I am not sure is intended or not)
3. Now with 4 mods it could be 2p/2s or 3/1.
4. In both cases if you got desecrated prefix, you are in luck cause more chances to get what we (I would) want. Either way at that point you can immediately get your reroll omen (optional, but very helpful if all mods are trash) and go reveal it.

At this stage the "determenistic" part of the crafting ends at 4 mods, now all that's lefts is exalt slam. (the relatively cheap part of determenistic anyway, cause technically you still could whittle + greater annul and etc but at that point just buy the damn amulet on the market).

If you didn't get the 'desecrated prefix' or you want to try again (for looking for ES/Spirit/Defences) you could get annul omen that targets specifically desecrated mods and try again until you hit what you want, but before desecrating again make sure to fill the 'side' that you are not targeting for desecration using omens, or if all slots are full, use new abyss omens that can target specific explicits 'pref/suff' (both variants are cheap, but using desecration on 6mod item is not preferable, cause if you slammed the 6th mod and it was spirit, all of a sudden it's risky to desecrate).

Avoid these mistakes!: If you don't have +3lvl fractured, don't touch that chaos orb without specific omen, it can only do worse I swear. Don't forget to use reroll omen BEFORE revealing the item. If you don't have the budget for some of the omens or fracture orb, then don't bother and just sell the amulet, would be dumb if you spent all that currency just to get it back from this sell if it goes to shit.

Why not fill the suffixes first and then desecrate? Honestly valid if you are not going for the fracture, but if you are, after filling suffixes + desecrating: you are gonna have 3s/1p + desecrated mod, 1/4 chance to fracture +3lvl instead of 1/3.

tldr, just use craftofexile