The spells have the most utility for the game and Clarity is an absolute must-have on Yuumi, especially since her mana is extremely low early on and, unless you build Archangel's Staff, you'll continually run out of mana.

Mid-Late game, you'll slowly deplete your mana since Yuumi's survivability is pretty good and, by the time Clarity comes off cooldown, you'd be around ~50% of your mana pool spamming Q and E.

Heal is great as a team utility spell + giving you a little extra healing if you take damaging procing your passive or mid-W. Since it heals when you're attached, it's a good way to keep your health up to prevent any AoE damage from W's, helps you be better able to detach for health relics, and gives you more opportunities to proc with more health.

Since you won't be taking much damage, you can be pretty lenient on when to use your spell. Closing a small distance with the short burst of movement speed is perfectly fine.

Archangel's Staff - Definite help with mana. I use the active whenever I W or try to proc passive. Enemies can still hurt you mid-W and the extra shields from the staff whenever you're detached is really helpful since Yuumi can be so squishy.

Athene's Unholy Grail - AP and Utility.

Ardent Censer - You'd be healing like crazy as Yuumi---the CD reduction, mana regen, AP bonus (which scales with your abilities), and the passive buff really makes ardent one of the go-to choices.

Redemption - You don't really need to be tanky as Yuumi but Redemption's active is really good, especially with the healing nerfs in ARAM and Yuumi's inability to heal multiple champions at once. Also, the stat bonuses.

Rabadon's Deathcap - You'd be accumulating a lot of gold as Yuumi from assists, kills with your Q (if you take Cut Down and build AP, even with Yuumi's damage and Q nerfs, you'd most likely be able to land a finishing shot on non-tanky champions), and from just staying alive with the ARAM gold generation. Rabadon's will greatly increase your heals and damage + helps out with your W, granting a bonus percentage of AP as AF.

Luden's Tempest - AP, mana, and CD reduction. You'd also be spamming your abilities like crazy later on so gaining stacks for Luden's Echo will be easy.

Elixir of Sorcery - Feel free to grab this if you've already built 4-5 items. Since you have so much survivability, you'd probably not visit the shop in a while so if you have enough gold to buy it but not another item, the boost is helpful. Also an end-game item.

You and Me! already starts at level one and Prowling Projectile can reach up to level six. You'd have to alternate between the two but finishing Zoomies first is a better idea since, despite ARAM healing nerfs, the damage nerfs to Yuumi makes you incredibly weak early on (your damage output is non-existent without AP items and since you won't be procing a support item, it's actually better to focus on Zoomies since your mana pool will be limited and Summon Aery can provide a temporary shield). Early on, it's better to time your E since it gives increased MS, a shield from your rune, and there's a longer cooldown. Later on, spam it.

Spam Prowling Projectile if you start to be accumulating mana mid-game since your Clarity will restore all your mana + the health relics (note: you have to be detached to get health/mana from the relic) + procing passive if you have the chance (enemy distracted, CC'd, alone, etc).

R to ward off enemies or root them in place to be killed by your team. Or do that last bit of damage and finish them off if you have enough AP and your target is squishy enough. Whichever works.

Transcendence and Absolute Focus could be interchangeable in my opinion. You'd ideally be over 70% health most of the time as Yuumi since you're going be attached + the heals and the bonus AP is very helpful in healing and damage, so I tend to prefer Absolute Focus.

On the other hand, Transcendence in ARAM is better than SR since you'd be hitting that level ten a lot earlier and you'd be benefiting greatly from the reduced CD around that level since you'd probably be spamming heals and Q's at or soon after.