Immediately after killing Hillock, search the vendor for any bow you can use and go with Galvanic Arrow. Prioritize getting/buying two Iron Rings, a Rustic Sash, and Serrated Quiver ASAP.
Your first Essence found in Act1 is best used on a Short Bow. Second Essence is best used on a Light Belt. Third Essence, prioritize on the first Sharktooth Quiver you get/buy.
These three items may well last you until the end of the campaign. Remaining Essences should be used on jewelry slots or your initial 4-links found as early as Act3.
Swap to Toxic Rain at or before getting Vicious Projectiles Support in early Act2. Your 3-links will be Toxic Rain>Mirage Archer>Vicious Projectiles, Toxic Rain>Ballista Totem>Vicious Projectiles.
Do the Library quest: A Fixture of Fate to unlock the remaining gems unavailable to the Champion. Purchase the following gems: Void Manipulation x2, Efficacy, Focused Ballista, Despair, Arrogance.
Starting in Act3, prioritize getting/buying two 4-links. Your 4-links will be Toxic Rain>Mirage Archer>Void Manipulation>Efficacy, Toxic Rain>Ballista Totem>Focused Ballista>Void Manipulation.
After getting your first Ascendancy point: First to Strike, Last to Fall, you'll need a 3-link, Arrogance Support>Defiance Banner>Vitality. Keep your Vitality gem at a level range that reserves nearly 50% of your total life.
The combination of Blood Rage and a Life flask (or Hybrid flask) will enable Adrenaline to be up nearly 100% of the time.
Withering Touch support will be the last gem you need coming in at Act4. It will be subbed in for Void Manipulation in your ballista link ONLY!
Acts4-10 require very little in the way of adjusting gear and or links. Toxic Rain does not require steady gear upgrades to function well. This is one of the best aspects of the build.
The only item you should bother purchasing prior to completing the campaign is a Quill Rain, which will ultimately carry the build all the way into high-tier red maps.
For early endgame mapping content, this build requires crafting the bow, amulet, and quiver.
Purchase a Porcupine bow (cheap 6-link ilvl 50 Short Bow). Hit it with Shrieking Essences of Dread until it rolls either +1 Socketed Gems, +% Attack Speed, or one open prefix with one open suffix.
Either way, isolate an open prefix and open suffix roll before moving forward. If no +1 Socketed Gems, benchcraft "Cannot Roll Attack Modifiers" and exalt slam +1 Socketed Gems. If no +% Attack Speed roll, rebench Attack Speed. Otherwise benchcraft +% Damage Over Time(prefix) or +% Chaos Damage(suffix).
Purchase an ilvl 82+ Agate Amulet. Alteration spam for T1 Damage over Time Multiplier. Augmentation & Regal Orb. If two open suffixes, protect a prefix slot (with a random benchcraft) and exalt slam the second suffix.
Beastcraft "Aspect of the Spider" for the final suffix. Metacraft "Suffixes Cannot be Changed" and Harvest Reforge Chaos. Assuming at least one open prefix remains, benchcraft -mana cost to skills. Exalt slam the remaining prefix if necessary.
Purchase an ilvl 82+ Sharktooth Quiver. Alteration spam for T1 Damage over Time Multiplier. Augmentation & Regal Orb. If two open suffixes, protect a prefix slot (with a random benchcraft) and exalt slam the second suffix.
Benchcraft "Cannot Roll Attack Modifiers" and exalt slam twice for guaranteed max life & bow skills damage rolls. Rebench Attack Speed or another craft that covers inconsistencies in attributes or resistances. (NOTE: the quiver slot can likely be bought for cheaper than crafted).
The Gull Helm will almost certainly be the most expensive Unique to get. It may be out of reach for some time, so be prepared to seek out an alternative helmet.
There is no important lab enchant for Toxic Rain. The best enchant will be an aura reservation enchant. As for the boots, +%damage leech is advisable as the only source of true leech in the build.
While not a true bossing build, this build is perfectly capable of killing all of the Pinnacle Bosses.