In his work Phaedo, Plato utilizes the character of Socrates, before his death by poison in prison, as a vehicle for establishing the existence of, and immortality of, the human soul. Though his arguments often make bold jumps that are difficult to reconcile, he does a more than admirable job of molding a logical argument for the existence of the soul, by taking on a number of possible objections to the theory, objections which are both abstract and somewhat scientific in nature. By likening the soul to the Forms, or the basic abstract properties of the universe, he argues that the soul not only must exist, but must also exist indefinitely, due to its very nature. This book is no doubt worth the read, as it provides an exceptional reflection on death and human mortality, and is a great starting point for Plutonian philosophy.
My reading in Plato begun with Parmenides. Which is pity, to think about it, since Parmenides is to this day considered to be one of the most esoteric. Contrast to Parmenides, where young Socrates stands up against this old thinker, Phaedo reveals old Socrates who now discusses things in fully down-to-earth terms. In fact, Socrates at this time is a dying one. And his tragic end is so well presented that it actually reads like a novel. Back to my point, this book is, I think, the most appropriate as a starter. Then you could trace back to Plato's more abstract discussions. Nowhere in Plato's works his conception of the idea is more clearly explained than in Phaedo. This also summarizes Plato's outlining of philosophy. A must-read.