It is the Federal Gov,
so it is complicated,
and you might want to Hire & Pay For professional help.

Two tips that trip many up:

Tip 1
There are other, lesser cost options, than the Typical Plan A

https://www.medicare.gov/supplements-other-insurance/how-to-compare-medigap-policies

Pay attention to Plan K and L as money savers if you are relatively healthy.

Tip 2
If you sign up for Supplemental (like AARP etc)
AT THE VERY FIRST
they must by law give you the lower cost “Community Rating” where they cannot look at your past medical bills
and just go by the national average bills of USA citizens at age 65.

If you sign up for Medicare Advantage Plans first
then get dissatisfied by the many restrictions
and want to switch in a later year back to “Traditional Medicare”
you will have to pay what will probably be a higher premium than “Community Rating” where they can look at your medical history.
This can be a “Big Deal” cost and surprises many.