Out of the three, which school would a nightblade use? I plan on starting a new Argonian Nightblade character.

I believe Nightblades use Illusion. You can do the others though.

I would take out destruction for a blade *night(blade)* and specialize in illusion over conjuration. Conjuartion is very helpful though.

From Morrowind:

Major Skills:

Mysticism

Illusion

Alteration

Sneak

Short Blade

Minor Skills:

Light Armour

Unarmoured

Destruction

Marksman

Security

From Oblivion:

Major Skills:

Acrobatics

Alteration

Athletics

Blade

Destruction

Light Armour

Restoration

My take on the use of Destruction in previous games is not so much the use of elemental damage, but rather making use of the "weakness to x" effects to enhance your ability to make a quick kill.

Illusion is a must. There's no need to explain why, it's fairly obvious.

There is no mention of Conjuration in the above builds because, as I see it, a good Nightblade doesn't need summoned help. They get in, get the job done and get out before anyone realises they are there. However, I tend to include it for the bound weapons and in the off chance you are discovered. Having some muscle to take the attention away from you is handy when you have pitifully low health.

I like the idea of a Nightblade with a Conjured Sword and Illusion combo. Destruction doesn't sound right IMHO but of course, that can be used as a backup plan

If anything, Illusion is your main.

Illusion it is then. I might throw in some Alteration as well.

Due to the nature of Destruction in previous games, it actually does fit a Nightblade. Many debuffs belonged to the Destruction school, plus touch range spells.

If you "have" to use Destruction with a Nightblade then I suggest using the Rune Spells. You would only need to invest in 3-4 Perks to use them effectively and they compliment a stealth based mage. Even more effective if you have the Quiet Casting Perk from the Illusion tree. Setting up magical traps is a very effective way to "thin the herd" from stealth. With the inclusion of Poison and Frenzy Runes from Dragonborn you can become a true Shadow Caster.

Definately Illusion.