Ancient Coin is the best possible starting item for Rakan's kit, and should be switched exclusively when a bad matchup or a bad carry require an alternate approach.

I hold onto my Warding Totem well into the laning phase most of my games, usually until I have 6 and can roam, but holding off on sightstone requires a good system of coordination between you, your carry, and your jungler to predict and prevent ganks without wasting vision timers.

Talisman of Ascension, Ruby Sightstone, and Mercury's Treads are my core items in every game. If you do your job well every teamfight should be a wipe and the enemy team might surrender before you get a chance to finish much else else. The Speed, Armor, Health, and Tenacity are everything you need to make your engages in teamfights count and still get out alive.

I Take Ardent Censer almost every game as well. The AP is essential for big heals and shields in mid-to-late game and it can be rushed after Sightstone if you don't find yourself needing the extra health from Ruby Sightstone urgently.

Redemption a good choice if you are looking to play passive, got Eye of the Oasis and need the HP, or if you're particularly good with the active. My general build assumes you've got a firm grasp of Rakan's kit and are playing to his strengths rather than covering your team's weaknesses. Redemption is a great support item, but Rakan's already got good AOE, sustain, and defense in his kit, so trading precious AP that makes all of that even better for 300 Health and some regen isn't worth it to me.

I have also recently found that taking The Dark Seal in early game and grabbing Mejai's Soulstealer as soon as it's stacked to 10 turns my games from overall successes to tremendous stomps. 125 AP, 10% movespeed, and the extra tilt you generate when the enemy team cannot kill you to save their lives is precious.

Situational Items:

Athene's Unholy Grail is a good buy when the enemy is AP heavy, and it can even replace your support item because of the blood charges passive granting a significant amount of healing on your Q -OR- your E.

Zeke's Harbinger is a good purchase to buff up your carries in lategame or when you need just a bit more armor, and the 20% AP bonus when charged is incredibly powerful in your lategame.

Abyssal Scepter, Mejai's Soulstealer, and Luden's Echo are good purchases for teamfighting and burst damage when the enemy has no way to stop your engages. Abyssal is best when you have AOE or burst mages on your team that can follow up on your engage and you can use the extra magic resist. Otherwise the movespeed and AP from Luden's Echo and Mejai's Soulstealer are incredibly powerful additions to your kit if you are staying alive during teamfights and are looking for more damage, bigger shields, and better heals.

Locket of the Iron Solari and Banner of Command are both good when you're falling behind in long games with heavy AP and AD respectively. Locket adds another significant shield to your kit and is great at preventing AP burst, and Banner helps you counter if your enemy has AP waveclear or a persistent splitpusher.

For my personal rune loadout
I take 3 AP quints for a needed kit boost through the whole game. Rakan scales well on AP, but it's not worth taking in Glyphs at the cost of defenses unless you get an all-AD matchup.
I take 9 Scaling Armor and 9 Scaling Magic Resist in my Seals and Glyphs to focus on mid and late game survivability. It can often be difficult to get strong engages with your lane partner in early game, but your sustain trivializes most pokes and trades in lane.
9 Flat Armor Marks make up for the early game disadvantage from my scaling Seals, and with Penetration or Attack Speed being the only other useful options, I prefer the defensive bonus so I can make more aggressive plays.
Flat Armor or Scaling Health Seals are both viable options, and Flat Magic Resist is good for laning against poke-heavy AP supports. Ultimately your runes depend on your enemy team's composition and if you prefer an aggressive or defensive playstyle in the early game.
As the Support, you don't need runes that focus on damage, and as a frontliner and engager you need to focus on survivability.

On Rakan the main purpose of your abilities is protecting and sustaining your carries while whittling down the frontline and waiting for an opportunity to engage and let your team follow through while you escape. Maxing E offers the most cooldown reduction, Q's healing is based on champion level rather than Ability rank, and W's rank only provides more frequent initiations and slightly better base damage. Since we max out CDR and we are a support, it's best to focus on defense in lane.

I used to max Q for poke damage, but Rakan is best played for sustain and defense during laning and then as an initiator for teamfights. I find it can be incredibly difficult to poke reliably in the earlygame with Rakan's short range, and the cooldown reduction on E is so powerful that by the time it's maxed it effectively matches the rest of your skill cooldowns. Maxing E leads to consistent, smooth combo executions because you will have it ready to get in or get out anytime the rest of your abilities are ready.

If you're far ahead or getting a lot of help from your jungle, you can max w for the cooldown reduction and base damage boost.
If you're against a lane that is easy to poke and your carry is trading frequently, you can max Q for the sustain.
Otherwise just play defensively until the teamfighting starts.

Your passive generates a shield that scales on 90% of your AP, meaning AP items generate a solid buffer for your engages to keep you alive even if your build is a little squishy. Its cooldown is relatively long, but every time you land an autoattack or an ability on an enemy, its cooldown is reduced. If you're tanky enough to stay in the action during the teamfight you may have your shield both during your engage and as the cleanup begins.

Your ability combos are relatively simple, and they all revolve around the concept of "get in, lock down, get out". Your most common combo is to E to whoever is closest to the enemy, W into as many enemies as you can catch, Q someone from point blank range, and then E back to your closest ally to AOE heal yourself and anyone near them. This can be mixed up a bit by saving both E dashes until after your engage so you can get farther out of the fight, and is best used when you take a lot of damage during your initiation.

The most important feature of your kit for teamfighting comes once you hit level 6 and have your ultimate. It synergizes with all the other movements from your abilities, meaning if you pass through an enemy while you use E or W, the charm applies. Ult before you engage and your enemies will not be able to escape your W as you pass through them, you can then charm the backline to pull them closer to your team, Q a squishy while they can't move, and E back to your frontliners to heal and shield them.

The same concepts can be used when the enemy team engages on you at a disadvantage. Use your ult to freeze their initiators, dive into the backline, and then sprint out and heal yourself while they attempt to make chase. This usually gives you good opportunity to kite them into an incoming jungler or laner and then turn once backup arrives.

I take 0/18/12 Masteries with Windspeaker's Blessing as my keystone and a focus on lane sustain and boosting my defenses and utility. If and when I see that my team has no tanks, I sub out for Swiftness and Courage of the Colossus so I don't die during initiations if my team chooses not to follow through.

Cunning:
Wanderer, Secret Stash, and Meditation are no-brainers for supports.
I take Dangerous Game over Bandit because Talisman is my primary source of gold income and the boost of health and mana saves my life in teamfights.
Intelligence beats Precision because more engages and more poke means more kills, where penetration doesn't affect your shields and your damage is mostly situational as a result of your crowd control.
The Defensive stats on Windspeaker's Blessing save carries every single game. Using your q heal in the middle of your team can give a tremendous defensive bonus to your carries before a fight breaks out, and being able to shield two people in short succession gives your front line better chances of survival when you initiate.

Resolve:
Unyielding beats recovery because of your Talisman's healing and every extra bit of armor and MR helps come lategame.
Siegemaster and Wanderer are both good picks, but your itemization should already give you all the movespeed you need, so I take Siegemaster.
Runic armor boosts your passive, your Q healing, Locket Shields, Talisman's minion healing, and more. Veteran's Scars' 50 bonus health isn't worth it.
Fearless is incredibly useful because of your tendency to tank some hits when you first initiate in a teamfight, and 2 seconds of extra survivability is usually all you need to get your full combo on and get out. Cooldowns for your summoners aren't as necessary because of your kit mobility, plus your shields and healing also significantly reduce the enemy's damage output so exhaust should be saved for shutting down carries that aren't currently under CC.