Original Medicare is the familiar program that's been around since 1965. In original Medicare, the government pays Medicare's share of your medical bills directly to doctors and hospitals. You can go to any doctor or hospital anywhere in the country that accepts Medicare reimbursement. That is nearly all of them.

But original Medicare is not free. You will still be required to pay some health care costs out of your own pocket. For instance,  people on original Medicare must pay a  $1,216 deductible for every hospital stay (rising to $1,260 in 2016). They must also pay 20 percent of the cost of most kinds of outpatient treatments, including doctor visits. And unlike the private insurance you're used to from your working years, Medicare does not have any limit on what you can spend out of your own pocket. The bills can mount up quickly, especially if you need costly treatments such as outpatient chemotherapy.

You may have a retiree or TRICARE plan that helps pick up some or all of those costs.

If not, you have two options for limiting your exposure to excessive out-of-pocket costs.

1. Medicare Supplement (Medigap) plans

These private plans cover most or all of original Medicare's out-of-pocket costs. If you select this option, you will continue to be covered by original Medicare. After Medicare has paid your claims, it will automatically forward them to your Medigap plan. The Medigap plan will then pay its portion of the bill.

Medigap plans do not cover prescription drugs. Therefore you must also purchase a  stand-alone Part D plan if you want drug coverage.

2. Medicare Advantage

Anyone on Medicare can choose to receive their Part A and Part B benefits through one of these private health plans instead of through original Medicare. Medicare Advantage plans now cover nearly 3 in 10 Medicare recipients. Most Medicare Advantage plans also include Part D prescription drug coverage.

With a Medicare Advantage plan, you continue to pay your Part B premium as usual. You may also pay an extra premium for the plan. You are not allowed to have a Medigap and Medicare Advantage plan simultaneously.

Medicare Advantage plans typically come with deductibles and co-pays. But unlike original Medicare, they have an annual out-of-pocket limit. That means that once you have paid deductibles and co-pays that add up to the annual out-of-pocket limit, the plan will pay 100 percent of your medical bills for the rest of the year.

Medicare Advantage plans work like the managed care plans you may have had during your working years. You will have to receive your care from doctors, hospitals, and other providers within the plan's network.

If you have a retiree plan, check with your plan administrator before signing up for a Medicare Advantage plan. It may affect your eligibility for your retiree benefits.

Once you are enrolled in Medicare, you can join, switch, or drop a Medicare Advantage or Part D plan once a year during the annual open-enrollment period, which runs from Oct. 15 through Dec. 7.

How to pick the best Medicare Advantage plan for you.

Here's a chart that summarizes the two choices.