What are the TNs for various spells? I know that the combat spells tend to go off of either Body or Willpower of the target, and Health spells tend to be based off of Essence (at least in the case of curative spells).

But what about the others? Illusions, manipulations (elemental and otherwise), detection (though I suspect it won't matter in the case I'm thinking of)?

If you have MitS, they are all listed at the back.

There are a few more factors than the magic category.

Initiative enhancer spells (health subset) are TN=reaction.
Elemental manipulations are TN 4 plus modifiers.
Indirect illusions are TN 4.
Control manips and directed illusions are mostly base willpower.
Telekinetic manips are usually 4 or 6.