Well I don't know if I do it correctly but for me it goes like this:
Conjuration: I don't use conjuration at all. In my mind I find it disturbing that you put up a wall of bodies/atronachs and you stay behind them casting your spells from a safe distance it almost negates the need for flesh spells,wards and healing (minus Soul Trap).
Illusion:I don't use illusion because I find it overpowered. You can dual cast Frenzy followed by Invisibility and be done with almost every opponent in skyrim. With 100 in illusion the game loses it's meaning you're a walking god among people. Some like this and I can respect that but not for me.
Alteration: I only use flesh spells and that's because I try to get the +30 magic resist. I also use them when I really need i.e. against bandits with weapons and not just any enemy just to increase it. I've used waterbreathing some times but that was like 5-6 times in a whole playthrough. I find alteration a bit useless but it adds a nice roleplaying effect in my character and the alteration tree itself is kinda nice.
Restoration: Anything that has the word "undead" in it is off of my list. Same goes for wards. Fast healing however is always in my favorites list.
Destruction: My absolutely favorite school of magic (oooh how original!). I use the novice,apprentice,adept and depending if I use shock or fire spells (I never combine two elements in my mages and I've never used frost) master spells except from runes. I only use what I'm given in the college for equipment so I don't go for the 100% magica cost reduction. The expert spells are only a bit more damaging than their apprentice counterparts but cost a lot more so in terms of dps apprentice spells deal more damage. I never had a taste for runes though and unfortunately I don't own the Dragonborn DLC to see for myself all the cool new spells.
I know that anyone who'll read this will disagree with me but trust me I have a lot more fun with depriving myself from going overpowered and following some sort of roleplaying path. I don't exactly roleplay but I try to keep it as lore friendly and realistic as I can that's why I use an altmer for a mage and never finish the main quest with. I actually don't even start it so I can't shout and don't become the dragonborn.
Personally, the spells I use the least are:
Conjuration: Bound Battleaxe, Flaming Familiar, Soul Trap
Illusion: Fear & Courage spells
Destruction: Walls & Runes, Freeze, Ignite, Whirlwind Cloak, Arniel's Convection
Restoration: Wards
Alteration: Transmute, Ash Shell, Ash Rune, Mass Paralysis, Equilibrium
I'm 100% certain they threw transmute into the game at such an early level and a minute from Whiterun just for mage characters. Spellbooks are freaking expensive, and you need that gold in early game to afford all your spellbooks. Mages are far more reliant on enchanted gear as well, even more so at lower levels, which again costs a ton.
Transmuting is one of the best ways to make money! You can sell gold ore directly to Pavo at Kolskeggr to bypass bartering price adjustment. And there are plenty of iron mines you can fast travel between to minimize exposure to scary things that want to eat your low-level wizard.