Talisman of Ascension is a must! It's Rakan's go-to gold item not just for the early mana regen, but also for the active ability to RUN AWAY from enemies. A good pinch item for when your team starts to disengage and you're all alone.
Ardent Censor, not just for the shield power boost, it also gives Rakan MORE movement speed. These two items alone make it possible to even run away from a YI!
Knight's Vow/Athene's Unholy Grail, the vow is generally good for if you trust your partner, and for the armor boost and health boost, otherwise go for the sustaining power boost of the grail. Not only have you been building movement speed items, but also mana regen. Those PLUS the grail make Rakan regen mana and health like crazy. Plus a little extra AP doesn't hurt him.
Redemption is a good final touch of regen and shield power making it the last of the core items needed for Rakan.
Boots ARE a core necessity, but I feel they get their own line of importance depending on the flow of the game. Heavy AD enemies you go for the Ninja Tabi, AP heavy of course the Mercurial Treads, but if you're doing FABULOUSLY and just want to wander and run circles around the enemy, Ionian Boots of Lucidity, not only for the speed but also Cooldown Reduction that Rakan needs AND reduced cooldown of your summoner spells. (If like me, you LOVE to use).
The last item for the Rakan build can go one of two ways. Offensive Luden's Echo for AP power spike and movement speed, OR Banshee's Veil for protection against enemy abilities.

And there you have it! See you on the fields of battle!