Kindred Mage-

This is equally as vital as Dual Casting for an Illusionist.  The ten level addition doubles with Dual Casting to 20, and stacking that onto the more specific level-affect boosts is exactly what you need to keep your spells relevant through the whole game.

Aspect of Terror-

Adding 10 or 20 levels onto the maximum affect level of your fear-inducing spells and places your Expert and Master dual-casts securely into the range to affect any humanoid or animal you care to try.  If you like watching things scream and flee, this is a vital perk.

Quiet Casting-

Since many Illusionists are going to be sneaking into range (and sneaking around in general), this is an absurdly useful perk, letting you stop to recast your Invisibility when it wears off without fear of being detected, and use your emotion-influence spells without being noticed casting them.  Since it causes all your spells from any school to be silent, there’s a ton of potential to use this with Conjuration to keep enemies under siege by atronachs and then zombies without any risk to yourself.  Alternatively, you can plant Rune traps all over the place undetected, escape to safety, provoke an enemy to move a little, then watch the mayhem ensue.  You can even use it to hide near a battle and let your follower fight while keeping them in peak condition at virtually no risk to yourself.

Rage-

The strongest of the level-affect perks, Rage grants an impressive 12-level cap boost to your frenzy-inducing spells, letting your Mayhem dual-cast spell affect any animal or human, and even pushing your two-handed Frenzy spell itself up to a cap of level 72 against people, and 68 against animals.