If you want to take your training to another level then you should consider getting some sort of training aid like a heart rate monitor or power meter to assist you. Heart rate monitors have been the standard for a long time now with the manufacturer Polar really leading the way. They have done a great job in trying to make the monitors more accessible and understandable for the average person. Heart rate is definitely your starting point to getting a better understanding of how you should train and how you can measure your effort and progress.
Power meters are a much newer training aid and have been used successfully by most of the pros to reach their specific training goals. But for the average person it is still expensive and debatable as to whether you will be able to get and make use of the full value that a power meter offers. Joe Friel author of Mountain Bikers Training Bible recently posted a great explanation of why a power meter is valuable for training and how it compares to a heart rate monitor. Basically it comes down to input(heart rate) and output (power), measuring one or the other will only give you half the picture, but measuring both gives you the complete picture. Check out his "Why you need a power meter" post for the full story.
But overall its best to start with heart rate and if you are just going for one of them then stick with the heart rate, it is more flexible to use on and off the bike, costs less and will definitely improve your performance.
