Lockstock, J. Crow's lugol solution is the most popular. It is a mix of elemental iodine and potassium iodide. I am biased in favor of potassium iodide so I've used liquid kelp to get it. I haven't read anything to exclude lugols solution. Some people use SSKI which is saturated potassium iodide. I would be more inclined to use it, rather than lugols, if I had to choose between the two, simply because I believe the iodide version to be easier to use than the elemental version.
Dosage is controversial. I've taken 50 mg of iodine daily, using liquid kelp, for 3 months. Then, I titrated down and now maintain with seafood. I estimate that I average about 1 mg daily now.