I only want my mage to use illusion for invisibility. What perks do I need to make that work well? I am low on perks with this build, and don't care about rage, fear, etc.

You just need the four reduction perks (novice-expert).

This and maybe Illusion Dual Casting if you want it to last longer.

If you're sneaking, it's probably best that you take Quiet Casting (only 3 perks) so you aren't detected after you cast it.

Do you (or anyone) have issues dual casting the invisibility spell? It sure works, but for aesthetics the left hand spell blob stays in the left hand and the right spell blob centers in front of the caster to make a strong spell. This is the only spell I've had issues with.

If you are a mage and have lots of magicka, invisibility may be useful without any perks. Base cost of Invisibility is 334 so its cost is 167 if your illusion skill is at 100. My typical midgame mage has 600 magicka, so I can use it once or twice to escape danger without cost reduction without feeling much constraint. I have to be sometimes a bit conservative about using it.

On the other hand I usually get the expert perk. I like invisibility much better when it's cheap.

I concur on both points.