I need advice. I'm really bent on making a Mage as my next character, since all my other characters have been of the "Battlemage" sort. This time I want something less akin to a warrior and more like a wise man with a staff, not too much armour (if any at all) but with good magical capabilities.

And I don't want the Absorption exploit, please. I'm prepared to play it in a really different way, more like a rogue and less driven to hack and slash. Any tips on character creation and play are welcome... Eg., how do you play a Defensive Class, like a Healer?

Yea, I'm not a fan of the absorption exploit either. Also, offensive magic has the tendency to get spammed. For instance, I tend to make little spells like this:

Damage health, 1-2 + 1-2 / 2 levels, area at range. It's the cheapest fireball you can make, and you can easily just use the "recast spell" button to fire off a barrage of these dinky fireballs at the floor in front of enemies. Even if they don't take very much damage, they really add up. And because of the area effect, even if they don't take much damage they are still knocked backwards by the blast--and pushing enemies into walls, whether by an area spell or a really good weapon hit, causes extra damage.

As defensive classes go, stealth can be greatly enhanced by a good shadowform, chameleon, or invisibility spell. Make sure you make them in the spell maker and pick the (true) version, because those will persist even after you attack! That makes it much easier to sneak into a crowded room and fight one enemy without the rest joining the fray. Shadowform is chameleon that only works in darkness and is thus cheaper--remember that dungeons are all darkness

Anyways, I don't do a lot of combat magic, offensive or defensive, so you'll do better to wait for someone like James Wildspell to pop in. Most of my magic is utilitarian.

Or nukes. Nukes are fun. Blasting your entire magicka reserve on one spell is pretty dang cool. Keeping a super-expensive and powerful reflect or absorb magic spell in your pocket can also be really good when you come across heavy spell users like liches, vampire ancients, and high level human mages. Blowing your wad on one spell is worth it if it renders their magic useless or self-hazardous in the process. Heck, sometimes it's the only way. Because those types typically have high spell resistance, casting spells on them isn't very effective; better to cast something on yourself that will help instead.

I've tried using Chameleon, and it almost never works. Somehow, the critter always detects me - the same with Invisibility True, alas. Once I attack a critter, it knows everywhere I move. And they aren't Undead or Daedra either.

I'm told that Stealth is good as long as you don't get near any light sources - cannot attest that - does Shadowform work or if you get near a lamp you'll get detected?

While funny, big spells are impractical against Increased Resistance / high willpower foes. This is just plain, old risk-aversion... if they save against the spell, we're screwed. Better to fast-cast a stream of those dinky fireballs that either hit or resist in turn, and widdle down an opponent piecewise. Usually we can back up while doing this, to keep them from dumping their magicka on the REALLY dangerous touch spells. Liches for example have Shock. I assure you all that while this spell svcks when you're putzing around Privateers' Hold at lvl1, it is 1-4/lvl and does not svck when used by a lich.