Some aquarists say that if you can't test for it, don't add it.
You may need to supplement calcium and magnesium if you have a lot of stony corals and water changes aren't replenishing them. I wouldn't really call either a "supplement" but more of a water parameter adjustment.
Not many people use iodine these days, as far as I know.
Phytoplankton falls more in the category of food than a supplement. It can help increase pod populations, but of course, will cause some pollution if it's not being eaten.
A lot of people add no "supplements" and have a perfectly healthy reef tank.
In a FOWLR tank, you probably won't need to add anything at all.
As you start to research corals, you'll find about their individual needs for food and light.
I personally stay away from any "magic potions" that are supposed to solve one problem or another, such as slime removers, "health" additives, etc. I feel that the less I add of unknown substances, the better.