Crook
The Crook is a necessary component for this archetype as it helps give your build the raw power it needs to unga bunga.
With the effect, "Your Weapons have +50 Damage for each Medium item you have.", you can grant a whopping +250 Damage across the board if you have all Medium items.
In terms of flat increases, its tough to beat within the first 10 days, but it can eventually get outscaled by other builds.
Phonograph
The Phonograph contributes to the Crook's AoE buff ability as a Medium item while funneling ramp into your main damage source with its cooldown reduction. Just stick it to the right of your most powerful weapon, which is the Lion Cane in this example!
Lion Cane
Lion Cane contributes to the build's Crook's engine as a Medium item and also provides scaling with its Max Health ramp.
The earlier you find it, the better as you'll get a big boost with every level up.
Atlatl
The Atlatl is often paired with Crook builds because of their inherent synergy. The Crook needs Medium items while the Atlatl needs a way to ramp its base Damage.
On its own, the Atlatl is incredibly slow, but with the effect, "This item's Cooldown is reduced by 1% for every 2 Damage it does." it can reach a 1.0 second cooldown (the lowest possible CD) if you get it to 180 base Damage.
Do note that in this build's particular run, Kripparrian managed to get a Shield-enchanted Atatl but it's hard to plan around consistently getting specific Enchantments. It's more of a bonus upside he managed to find but not necessary to pulling the build off.
Belt
Your last Medium item is the Belt, which synergizes perfectly with your Max Health stacking. It's simple, but a strong inclusion!