PROS

+ Late game monster.
+ High burste.
+ Free Guardian Angel with her passive Rebirth.
+ Strong waveclear.
+ Her W Crystallize can turn teamfights in addition to her high damage with her R Glacial Storm.

CONS
- Very mana dependent.
- Weak early game.
- Easy to learn, hard to master.
- Immobile champion with only escape tool being her W Crystallize.
- If messed up hard to recover.

Flash

This is the best 1st option because Anivia is immobile and Flash offers engage, disengage and escape. Overall a must have.

Ignite

Provides Anivia with a bit more burst to take down targets and scales really well with Electrocute rune page. Also when laning against champions with a lot of healing helps also with the grievous wounds it applies and making them more vulnerable to you.

Teleport

With Teleport you can return to lane faster and lose less exp and gold. Also you can help out your team by roaming and snowballing other lanes. It is very efficien again heavy roamers like Akali and Talon and you can even counter-roam them.

Exhaust

Very good vs high burst champions because you catch them off guard by reducing their damage and also you can slow people to make them stay longer in your R Glacial Storm

Electrocute can be easily proced with Anivia's kit and offers high kill pressure. You can combine it with the burst from your E Frostbite to burst the enemy down. Easy combo to proc Electrocute is Q Flash Frost stun + auto-attack + E Frostbite. You can also take Ignite for maximum kill pressure from level 2. Arcane Comet is also an option for poking usually in harder matchups and can be easy to land with the stun from your Q Flash Frost.

Cheap Shot is perfect to use after the stun form your Q Flash Frost or after a fully formed R Glacial Storm. The true damage feels really nice when proced with E Frostbite and apply the damage from Cheap Shot and E Frostbite burst.

Eyeball Collection is a scaling rune essential for Anivia as she is a scaling champion. It offers free AP per takedown and bests every other rune of the category due to the fact that you need every help you can get to scale and not fall behind because it will be very hard to come back.

Relentless Hunter is also the best option of the category since the healing from Ravenous Hunter is kinda pointless for an AP mage like Anivia since others will be peeling for you. Ingenious Hunter total waste since no active items (yes i know the Zhonya's Hourglass has an active but it is not enough reason to take Ingenious Hunter just for it), and Ultimate Hunter again pointless since R's Glacial Storm CD is very low. So we chose Relentless Hunter to help her roam (because she is very immobile) even when Teleport is on CD or not picked at all.

Presence of Mind as stated previously Anivia is very mana depended and this rune helps with regeneration a lot on damage or takedown of champions.

Coup de Grace deals extra damage when enemies are below 40% health. And the whole point is to burst enemies down so this rune will be very usefull.

If you Teleport right before your health reaches 0 and your passive is triggered, the Teleport will not be canceled and you will actually tp as an egg.

You can use your W Crystallize to make the enemy move to a certain way to hit both your Q Flash Frost and E Frostbite