I think before picking any particular philosophy, it's better to aim for a broad understanding of the history of philosophy, particularly as it has developed in the West. I also highly recommend Sophie's World: it is a very entertaining novel, and all the while offers in simple language a very good understanding of some of the core ideas of important philosophers. Once you become familiar with what philosophy is all about, you can either
1) pick a more thorough treatment of its history by reading Russell or Durant's books,
or 2) start reading some of the essentials.
Here is a pretty standard road map: Plato: Republic
Aristotle: Nicomachean Ethics, or Categories and Metaphysics if you are brave)
Hume: Treatise concerning human understanding,
Kant: Critique of pure reason,
Schopenhauer: The world as a will and representation,
Heidegger: read being and time if you are brave, otherwise at least read a few of his essays such as the origin of the meaning of art, or the question concerning technology.
You also need to read commentaries as not all of these texts are accessible, but get used to, and don't be afraid of, reading original texts, for which there is no substitute. A great collection of commentaries on various subjects is Stanford's Encyclopedia as well as Cambridge companion series.
You may find some of these philosophers (e.g., Heidegger) to be outright lunatics, but do make an effort to read something from them.
Lastly, this is not an easy journey and will likely take many years, and you are more likely to give up in the middle. But even if you do, you will probably come out with something valuable. Remember that philosophy is an activity.