Hi ya Peach, I began riding two years ago at age 71. Good move deciding to get out. Good advice here on selecting a bike. Right off the bat, the kind of bike that could carry you in le Tour can be safely dismissed. The mountain bike that some may wish to ride on the Continental Divide in Colorado can likely be dismissed also as being too specialized. In between seems a more likely range of utility.
These middle category bikes are sometimes called comfort or commuter types. You would see many of them on a local bike path or on the way to the train station ridden by commuters. They have a more upright position than race bikes, are usually lighter than mountain bikes but still have somewhat fatter tires than the race bike. The illustrations above cover these distinctions well.
The best thing you can do is visit several bike shops to look the selection over. You at that time are looking over the bike shop itself and judging their advice and level of service. All bike shops will carry good quality bikes that will provide years or thousands of miles of service.