I also turn 65 in January. So, Medicare comes into play on January 1. I have already received my Medicare card that shows me enrolled in Parts A & B.
This week, I signed up for Plans D & G.
You are right that you will get bombarded with mailings.
I stayed away from the Medicare Advantage plans that most of the insurance companies are pushing for a couple of reasons.
First, is
HHS Report: Medicare Advantage Plans Deny Some Needed Care.
Second is that I wanted some coverage for when I would be out of the country. Plan G was the only real option for this for me. Plan F was not available to me since you needed to be enrolled in Medicare prior to 2020.