I have found Calm to be the most useful of the starter spells. You should take the Dual Casting perk, as that 2.2 times the effectiveness level, so from level 9 to level 19 (rounds down), add one perk from the center line (Hypnotic Gaze) to make Calm spells more effective, so from 9 to 17, then dual cast hits to level 37, which will take you very far into the game with just 3 perks (4 if you need to take Apprentice Illusion).
To level it up, use any Novice spell you want, and yes, casting Fury twice on an NPC counts as 2 casts and gives you experience for each cast. I think it's best to use Calm, so you can let your magicka regenerate the whole time the enemy is Calmed, then when it wears off cast it again.
Once your level is high enough, you will be able to purchase Muffle from the court mages, and Muffle is the absolute best way to level Illusion quickly. You can cast Muffle when you aren't even near any enemies, and it levels your skill very rapidly. You can take the Mage Standing Stone, and/or purchase a bed at the inn and get the Well Rested bonus for more experience.
As far as perks that are really worth it, I would say you can take up to Expert Illusion, Dual Casting, and either the center line or the right line up to Master of the Mind. When dual casting, you should be able to hit almost everything in the game with the Pacify and Rout Expert spells, and Frenzy Adept to a slightly lesser extent. The Master spells take up two hands and can't be dual cast, so they are actually less effective at hitting higher-level foes. With the center perk line only, Hypnotic Gaze boosts your Pacify to 28, then dual cast that to hit level 61 foes! A Draugr Death Overlord is level 45, and a Dragon Priest is level 50. If you don't take the Hypnotic Gaze perk, a regular dual cast Pacify will hit level 44 opponents.
The right side of perks includes Quiet Casting, but only Animal and Human effectiveness boosts, so once you get Master of the Mind, your spells won't be boosted when hitting undead, unless you took the Restoration Necromage perk. I would say it's really your preference as to which side you want to take (center or right), but you really don't need both of them unless you want them.
I think the best spells in Illusion are at first Calm and Muffle, then Invisibility and Pacify. You can also use Fury and Frenzy, but Frenzy has a lower effectiveness than Pacify and Rout. Frenzy is up to level 14 instead of 20, and it's boosting perk Aspect of Terror boosts 10 levels, so 24, dual cast, will hit level 52 which is perfect for end-game, but until you get to the Aspect of Terror perk it will be hitting lower.
One other interesting thing to note is that if you are using Destruction, Aspect of Terror actually adds 10 flat damage to every fire spell, and is affected by the 50% Augmented Flames perks, for a total of 15 extra damage on every fire spell. I am unsure whether or not that glitch has been fixed.
I hope I answered your questions, I may be a bit biased, and long winded unfortunately. Let me know if you have other questions.
