Yep, no matter what, there is a minimum payment that comes out of your social security payment. It's a hard number: $174.70 per month if you make under $103,000 per year. $384.30 if you make more. These are not means-tested in any way. They apply across the board to everyone, no matter which type of plan they get (original Medicare, aka PartsA & B, or Medicare Advantage, aka private plans, Part C).

If you get Parts A & B, the only possible route to full coverage is Medigap, which are private plans. The Medicare Advantage Plan I chose was from Kaiser, and had no additional premiums. I did a little research on them and the Georgia version has a pretty good reputation.