If you are going to use a body composition monitor, look for one that includes the upper and lower body. If you get one combined with a scale that you step on, get one that includes the hand held sensor so that your upper body is included in the measurement.
Accuracy depends. A monitor can over-estimate or under-estimate, but if you are using it to track your progress, ie are you improving over time, then they can be a useful tracking device.
Units do have memory for different periods of time such as up to 90 days.
For more information on measuring body composition, you will find a lot of helpful information here: How to calculate Body Fat %