At age 60 generally it's not that hard to get life insurance assuming you are still healthy. As far as what to get you have several options to choose from, including:
1) Term Life Insurance -- Generally term life is the least expensive policy, A term life policy is only in-force for a set amount of time "term", at the end of that term the policy will increase in price considerably. Therefore you need to get the longest term possible to lock in the price if your need for life insurance is going to be for the rest of your life.
2) Whole Life Insurance -- Generally whole life is the most expensive type of life insurance. Your whole life policy is in-force for your entire lifetime or until the endowment age at which time the life insurance is paid directly to you if you have survived. Whole Life insurance builds cash value inside the policy over time that can be borrowed against, or the policy can be cashed in if you no longer need the life insurance protection.
Also, there are some life insurance plans that do not require you to take any physical examination to qualify, but they usually cost more.
Learn more about life insurance for people over 60 and compare plans.