First, make sure your diet is a healthy one. By 60, many people have developed eating-related health problems. Failure to notice these problems could adversely affect your chances are becoming fit.
Re-discover your limits. It's been a long time since you've been exercising, so you really need to know what you're able to do. For some exercises, it can be easier to discover your limits with a partner.
Check out alternative exercises, especially low impact exercises. As you age, your bones may weaken. In addition, your joints may ache and your cartilage may be worn. Low impact exercises can often give the same level of exercise with reduced stress on the target area. For example, an elliptical machine is a great alternative to a treadmill.