If you are drawing SS now, you should get the card in the mail that bibmisi described. That's my experience too.
Before Sharon retired I was on her Maine state public employee health care coverage. After she retired the benefit was very expensive to carry a spouse, her rate was fine, but to keep me on it was astronomical. I don't think they wanted me. :laughing:
It pays to shop around. I have Medicare A & B, plus an extension to B which includes D. The extension plus D cost is $54/month and provides the coverage I need. What you need may differ of course. This is from Martin's Point, a small Maine-New Hampshire company I didn't know much about but they checked out. The cost is well below any AARP sponsored plan or other big-name insurers.
Did it all on-line too, and all the medical people associated with our local hospital are preferred providers. The only thing different I did was move my prescriptions from Rite Aid to the grocery store because that grocery chain is their preferred pharmacy in Maine and the co-pays are lower. Plus I stopped paying Anthem ~$300 per month for an individual policy with a $15K deductible.
In any case, every year Oct to mid-December you can make changes to your selected carrier and coverage if you are on Medicare. So, it isn't as if you are making a decision you have to live (or die

) with forever with private insurers. The state plans may not be so flexible in that regard. I think you need to begin by completely understanding the state plan and go from there.