Meditation is very dualistic in many ways.
The best way to meditate is to not try, the best mind is no-mind, the best way to reach enlightenment is to not strive for it.
Spanishflea, you are on the right track when you say you should be discovering who you really are. It is in fact very special that you allready have this feeling after just a few meditation sessions !
However, you will never discover the true you by thinking about something, or anything for that matter.
You see, there is a difference to be observed between "you" and "what you think about". In fact the very sentence says it: "What you think about".
The "you" is considered to be seperate from your thought. Your thought is supposed to be a tool for the "you" to help you accomplish things in life. Unfortunately, even tho we feel that we control what we think about, it is the opposite. Thought controls us.
An easy way to demonstrate this is to try to not think anything for 30 seconds.
Try it !
If you fail, you need meditation.
If you succeed, can I become your student ? You have mastered enlightenment !
Enlightenment starts with becoming lighter from the burdons of thought. "the thinking disease" it is often called.
Because the mind is constantly racing thoughts through our mind, we think that we are what we think. Even tho we become what we think ( check out the LoA threads, as a man thinketh ) it is not who we are.
The real You is obscured by all those thoughts and emotions. By meditating, we learn and train our mind ( gently as there is no other way ) to not constantly identify with thought, to create space between who we are and what we think or feel.
In time, thoughts and emotions will be seperate from our deepest self, a state commonly described as enlightenment.
As you might have guessed now, the trick is to not think. Since this is almost impossible to achieve without practice, we learn tricks, commonly known as meditation techniques, such as watching the breath, mantra, chanting, prayer, you name it. By slight concentration on one thing, you train yourself to watch all your thoughts, observe them without judgement or involvement. That is all you need to think of, nothing more, and I must say, it is difficult enough allready.
I wish you more wonderfull meditation sessions