There are two basic kinds of pedometers: dial read out or digital read out. The most basic pedometer of either kind shows the number of steps you take. That's all you need for your intended purpose.
There are many other features available on some pedometers. The first to look for is stride length. This allows you to get a more accurate idea of the distance you've walked. Depending on your needs, you may want a large screen display to see the numbers easily.
If you walk in the early morning, at dusk, or at night you can get a pedometer with a light. Other features include memory, time of day, stopwatch, even an alarm, or a radio. Be sure and ask if there is a leash, clip, or belt clip to attach the pedometer. Sometimes one of these comes with the basic unit. Sometimes it's ordered separately for an additional charge.