Originally Posted by MadKaw

There are two types of medigap coverage. Medicare Advantage and Medicare Supplement. As a rule of thumb, if you are healthy go with Advantage, if not, go Supplement. You can change during open enrollment once a year. Your company coverage may be one or the other of those, and all you need is Medicare Basic.
Like you said, talk to HR. The people at medicare see their job as reducing medicare costs by confusing people so much that they die. (That's 78% a joke, but dealing with them can certainly be frustrating.)

You must sign up for medicare when you turn 65 or face heavy penalties. If you are still working and have coverage from your employer, you can waive coverage (and attendant cost) but you must sign up.
You do not have to take SS until you want to. The longer you hold off, the larger your benefit, but it is a matter of balancing months of benefits vs. amount of benefit to figure out what is best. Either way, it is a gamble.