You sound like how I was. I went back and forth for a month before I took the plunge. I was afraid of detox and the supplement list was overwhelming, but I started them weeks in advance to get in the routine. The supplements, as I've found out, are the basic ones that we should all be taking anyway.
I think your current cleanse may be beneficial in dumping a lot of your toxic load now and may help with less detox from iodine... I have friends at work who wanted to start Iodine a week ago and i told them all to do a month long cleanse of the bowels, liver and kidneys before even attempting it. When I started the Iodine it was 2 weeks after my cleansing ended and I do believe it was perfect timing because I was able to start Iodine with only very mild detox. I had a few pimples around my collar bone and a chest cold kind of reaction. That was it. It's hard to predict what detox might look like, but it seems to go through your weakest organ. Mine was my lungs. I know from speaking with you before that you have digestive issues, so your detox may manifest through your colon, which is a preferred detox organ. I have found iodine very beneficial for my past muscle and joint injuries from gymnastics and haven't needed to wrap my ankles or wear a knee brace in weeks... so you might be surprised and find much relief too.
The female body needs the elemental iodine for the female organs, so Lugols is a good place to start because it contains both elemental iodine and iodide. As to how much, that will have to be your call. Sometimes small doses bring worse detox and larger doses will skirt through detox. Sometimes people dont do well with large doses and sometimes those who start out large to lessen detox can drop the dose down later. I started at 120mg and couldn't have asked for a better experience.
The most common complaint is headaches and the people here can walk you through almost anything.