If you do not mind not being a pure mage - under Conjuration school there is Bound Bow and if you have the Dragonborn DLC, Bound dagger. These spells will affect and are affected by Conjuration and Archery/One Handed. They also receive sneak attack bonus as physical weapons would which makes good choice of spell for mages to initiate an attack.
Using the weapon itself will produce no more noise than a physical weapon. So even without Quiet Casting, you can summon the weapon from a distance and close in for the attack - just make sure to note the summon duration of the weapon, if you take too long the weapon might unbound.
If you wish to purely rely on the five schools of magic - spells like Firebolt and Ice Spike can be used over long distances, but to practically fire it without Quiet Casting and without being heard, you will need to cast from distances where the target is barely visible. So you will need to invest in Illusion school for the silent cast and you have to cast from behind/ out of the line of sight of your enemies.
Note that while the perk will hide the noise from your spell, most spells produce light which will increase detection from your enemies so you need to cast from outside their line of sight to ensure they do not spot you visually.
Tactically, you can use the Magelight spell from the Alteration school while hiding in cover to draw you enemies' attention away from you then cast a spell from behind them followed by Muffle and/or Invisibility to sneak away before repeating the process. Important that you DO NOT cast the Magelight within the line of sight of your enemies, the increase the light around you at the point of casting will almost immediately give away your sneaking attempt. Do so from cover so that they will investigate the light and back-face you instead.
The runes spells from Destruction school can also be used for sneak attacks, you have to watch the movement route of your enemies and plant it along that route, retreating away before they return to step on it while patrolling. Alternatively you can plant a rune near a pillar/wall and lure the enemy to it using Magelight from cover This tactic will greatly reduce the chance of being detect since you can almost be fighting while physically be behind cover.
Another viable tactic is to use Paralyse, though this can only be done with Quiet Casting since you have to be relatively close - definitely within audible range, to cast paralyse. But if you do it with silent cast and from behind the target, the target will be unable to move for a few seconds, granting you enough time to blast another few spells and retreat away before the target can move to find/chase you.
Be careful to watch for the direction the targets fall while you do this, sometimes it might fall into a position where it can visually see you. That will enable it to detect you while you try to blast it with spells due to the proximity - you are already quite near to it to cast Paralyse and light from your spells.
While this is not entirely stealth, the summons under Conjuration school and the Frenzy series of spells under the Illusion school can make the opponent distracted while you blast them from afar. With sufficient proficiency in Sneak, there is a chance that you actually remain undetected while you hit them with your spells.
If bound weapons are used there are certain(?) conditions that might trigger the sneak attack bonus even while you opponent are engaged in battle - though I have yet to confirm how this works but I have successfully triggered sneak attack bonus on several occasion using this method.
This method might potentially kill the target fastest but will require a high proficiency in Illusion. The Calm series of spells includes Calm, Pacify, and Harmony. While Harmony will be more effective and useful in most situations, it requires a longer casting time plus more magicka. When the level of the enemies get higher you might need instead to use Pacify with Dual Casting to calm the target.
Practically, this method is rather simple - hit the target with the most painful spell you can cast, calm it down, repeat. A calm target even if it detects you will not attack, therefore you can just casually move into position and cast another spell to hit again. If you are using bound/physical weapons to damage it will also be very easy to move out of the enemies detection to hit it with sneak bonus.