Build 1 sports an impressive early game with cheap and easily affordable items. The triple Doran's and the Wriggle's Lantern will give an early game advantage. By providing attack damage, life steal, health, and armor, farming will be made extremely easy. Furthermore, wriggle's lantern unique passive and unique active helps to provide a safe farming environment. A free sight ward, provided every 3 minutes by the ward, can be used to protect the lane from enemy ganks.Because Phantom dancer is a solid item that provides several factors that are required by any ranged DPS carry: Attack Speed, Critical Strike Chance, and Movement Speed.
Build 2 + Build 3
Build 2 and Build 3, usually a standard build, provides everything that is required for a ranged DPS. Infinity Edge provides a substantial amount of damage and is a core item in any ranged DPS build. It also provides a 250% critical bonus. However, Infinity edge is created using very expensive smaller items (Such as the BF Sword) that may stutter your build.Zeal is also a core item in a ranged DPS build. It can later be upgraded to Phantom Dancer.
Build 1 VS. Build 2 and Build 3
Although the more popular builds (2 and 3) provide a ranged DPS with everything that is needed, Build 1 provides much more than build 2 and 3 with a much more efficient price. (Items are made up of smaller parts and are easily affordable) Compared to build 2, build 1 lacks 37 damage (47 in build 3) and 5% critical strike chance. However, it makes up for its lost by providing 200 additional health, 30 armor and 21% more life steal as well as 35% more attack speed and 7% more movement speed. The effectiveness of having all of these bonuses outweigh the lost of 37 attack damage and 5% critical strike chance. The armor provided by build 1 makes the damage gained from build 2 unnoticeable in any exchange.
The critical chance is far too low to deem the passive of IE dependable. And if it does deal a critical, it will only deal 50% more damage (from your base attack). (So if you deal 200 damage regularly, you will deal 400, with IE you will deal 500. However with the armor and extra health from Build 1, you will easily sustain through it. This is further backed up by a higher sustain from Doran's Blade and Wriggle's Lantern. (Dramatically more Life Steal)
Build 1 is slightly cheaper than Build 2 and is slight more expensive then build 3. However, its productivity is much more than build and 3, make it a much more cost efficient choice. Each ward provided by the wriggle's Lantern is worth another 75 gold, making you 75 gold richer every 3 minutes that past (As long as you continue to effectively use the active)