Before I go any further I would like to "clear-up" what I hear people say over and over again including Social Security so to set the record straight, on page 11 bottom left of The Medicare and You Handbook in the third paragraph it says "unless you have supplemental coverage-like Medicare Supplement Insurance (Medigap)."
In the fourth paragraph last sentence - "Or, you can use coverage from a current or former employer or union, or Medicaid."
On your Medicare Card it says Hospital Part A and Medical Part B which is two parts - Second paragraph second sentence "If you choose to join a Medicare drug plan, you'll pay a separate premium for your Medicare drug coverage (Part D)." If you don't sign up for Part D, you get penalized monetarily for not having Creditable drug coverage as it states in Section 6 page 79. It's optional and offered to everyone with Medicare. Most people at some point end up "needing" Part D.
Lastly - if you don't sign up for Part B when eligible there could be a late enrollment penalty - see page 23 in blue "Important!"
The point is, a Supplement is "secondary" coverage to Medicare such as: Current or former employer or union coverage, Medicaid, Medigap known as Medicare Supplement or (Medicare Advantage Plan with or without prescription drug coverage also known as Part C - you give up Original Medicare joining a Medicare Advantage Plan with or without Prescription Drug Coverage).
Let's discuss what makes sense financially for you.