You forgot the best class. Fisticuffs. Argonian or Kahjit for the added unarmed bonus damage. Argonians get 10, Kahjit get 15. Skill trees inlcude Heavy armour, smithing, and enchanting. Max your smithing and heavy armour as soon as possible for two reasons. The heavy armour perk for your gauntlets doing their base armour rating in unarmed damage is god teir with dragon or daedric armour. Enchanting combined with the gloves of the puglist disenchanted, found in the ratway sewers, at max level, can be applied to a ring, a necklace I believe, and your gauntlets, for a grand total of an extra 36 unarmed damage. The enchanting can also be applied to your armour to make up for some of your weaknesses. Let's do some math. Assuming you went kahjit. 15 unarmed damage. Base level dragon bone gauntlets do 90 damage. Rings and enchanted armour at 100 enchanting add 35 damage. All for a grand total of 140 damage. Fists are the fastest form of attack method in the game meaning that you can do 140 damage per second. And, for additional kicks, take the perk in the vampire skill tree that gives your unarmed attacks poison damage. You now have the ability to fist everything in Skyrim.

Does anyone know if it's possible to make an effective, stealthy mage/combatant? As in, stealthy, but with a one-handed weapon and a spell in the other (typically)?

Milk drinker would suit you

Blood mage on Skyrim? Vampire?

Never played skyrim is it fun

Nightstalker as it will be the void hunter subclass

BE EXCALIBUR FOOL! USE DEM RADIAL JAVELINS