If you're using fossils, get a weapon that is ilvl 75+. If you're using essences, ilvl doesn't matter.
The weapon doesn't need any influence, just a normal/magic/rare 2-handed sword/mace/axe. Buy it already 6-linked, they are cheap, like 10-20c. And get something that is easy to color with chromatic orbs. So if you're doing this build, probably a weapon with lower dexterity and higher strength requirements.
It should cost less than 11-12ex to craft it yourself, unless you're very unlucky. Essences will be cheaper than fossils, but you can't get max minion damage with essences.
The biggest costs are the crafting bench mods. "Cannot roll attack modifiers" (1ex), "Prefixes cannot change" (2ex), "Can have up to 3 crafted modifiers" (2ex), "+2 to level of socketed support gems" (2ex). That's a total of 7ex. The rest of it can be done for probably under 1ex, maybe 2ex if you're very unlucky. So probably 8-9ex total.
Unfortunately, if you want minion damage, you have to use essences or fossils. Minion damage is a special mod that isn't part of the regular pool, so you can't augment/alt/regal minion damage onto it.
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However, I think Rex_Banner's idea would work and be extremely helpful. I'm going to gather some fossils and try it today. But it would ONLY work for maces, swords, and axes. It will NOT work for warstaffs (warstaves?), because warstaffs have extra non-attack prefixes. It goes like this:
1. Fossil/essence craft until you hit the desired minion damage. You'd probably want T1 damage for this.
2. If there are extra prefixes that aren't "+1 to Level of Socketed Gems" try to annul the extra prefixes. If you annul minion damage, return to step 1.
3. If there are three suffixes, try to annul one of the suffixes. You need a free suffix for the crafting bench. If you annul minion damage, return to step 1.
4. If you already have the mod "+1 to Level of Socketed Gems," go to step 7.
5. Craft "Cannot Roll Attack Modifiers" on an open suffix.
6. Use the beastcrafting recipe "Add a Prefix, Remove a Random Suffix," to add the prefix "+1 to Level of Socketed Gems." The beast you need is a Farric Wolf Alpha. Currently, they are going for 33c in Metamorph League, so it is much cheaper than slamming this prefix with an Exalted Orb. This cost-saving measure was suggested by floodo1.
(See Spoiler for an alternative to step 6.)
Spoiler
(Alternative 6.) Slam the prefix "+1 to Level of Socketed Gems" with an Exalted Orb. If your weapon has three suffixes (including the crafted "Cannot roll Attack Modifiers"), then this should only take 1 Exalted Orb. If you have open suffixes, this could take a few exalted orbs if you keep slamming suffixes. Steps 5 and 6 were suggested by Rex_Banner, it works for 2H maces/swords/axes, because there is only one non-attack prefix.
7. Right now you should have a weapon with 1-3 suffixes and only 2 prefixes: minion damage and "+1 to Level of Socketed Gems." If your weapon has any suffixes other than "Cannot roll Attack Modifiers," then go to step 8. If your weapon has no other suffixes, remove the crafted mod by using the crafting bench, and go to step 10.
8. Replace the crafted mod "Cannot roll Attack Modifiers," with "Prefixes Cannot Change."
9. Use a scouring orb on the weapon. This will remove all of the remaining suffixes. Note: Only do this after you have crafted "Prefixes Cannot Change"! Otherwise you will wipe every mod from your item and be back at step 1!
10. You should now have a weapon that has no suffixes and two prefixes (minion damage and +1 socketed gems). Time to multi-craft. Craft "Can have up to 3 Crafted Modifiers" onto the weapon.
12. Craft "+2 to Level of Socketed Support Gems" onto the weapon.
13. Craft "Minions have % increased Attack Speed / Minions have % increased Cast Speed " onto the weapon.
14. Congratulations! Your weapon is complete!
