A couple notes:
1) Gloves of Belligerent Skies don't work with damage from lightning charges. I tested this and the wiki confirms it. Maybe they've changed it in a patch. Spellsparkler can be good for damage and hit chance, but that's it.
1.5) Boots of Stormy Clamour don't work with Corruscation Ring either.
2) Amulet of Elemental Torment has been moved to act 3, Hope has it (you have to knock her out I think).
3) I recommend just putting on Risky Ring as soon as you get it. The comfort on having a 90%+ hit chance on every ray is fantastic, assuming you can kill or disable your enemies quickly enough. And it helps so much with stacking acuity. I hate how often Spell Attacks miss in this game, and Warlock is the prime example.
Worth mentioning are Gloves of Battlemage's Power, which you can find in the tollhouse in act 2. They add 2 Arcane Acuity for every Booming Blade and Divine Smite, including Divine Smite as reaction. So with the Helmet of Arcane Acuity you can do Booming Blade, then Divine Smite on another attack and get at least 8 stacks. Divine Smite as reaction adds another two, there's no limit per attack.
The gloves are bugged, meaning you will often get more than expected. Tons of effects, like Luminous Armour explosions or just throwing a healing potion give you Acuity.
So with these and the helmet you can get 10 stacks in 2 attacks and then either quick cast command or if you have Band of Mystic Scoundrel you can upcast Extended Command with bonus action.
I think this could be a good control build too. With Helmet of Arcane Acuity, one volley at 5 enemies gets you +10 spell save dc instantly. Then with Band of Mystic Scoundrel you can either upcast command (though only level 3) or cast hold monster from scrolls. Downside - you won't have arcane synergy, but you wouldn't have high wisdom anyway, maybe 18 and that's only with Khalid's Gift.
For control, Helldusk Gloves, Cloak of the Weave, and Landfall Armour would also help with dc a little. With these, 18 wis, +10 arcane acuity and resonance stone you should be able to paralyse everyone.
You can give this build Helldusk Helmet. It's bugged so it doesn't give true darkness immunity, but it prevents blindness anyway, so you can attack in melee as if you were immune to darkness. So it can work very well with a darkness party.
Also if it's your main character and you go for the 8/4 variant, you can get 24 wisdom: 16 + 2x ability improvement + ethel's hair + khalid's gift + mirror. Very nice to have.
In Act 1 and Act 2 a good armour is Infernal Robe, Wyll gets it for killing Karlach. Then Graceful Cloth can go to your archer.