I use the same type/weight of thread for the bobbin as on top. The reason for that is just that it has worked for me and then I don't have to buy as many different types of thread.
Whether I use the same color depends on the situation. For things where the thread won't show, I often use up old bobbins and they usually don't match. For quilting, I'm usually trying to blend into the fabric, which frequently means using different colors on top and bottom.