In a sense it would be inappropriate to speak of "Hegel's system of philosophy," because Hegel thought that in the strict sense there is only one system of philosophy evolving in the Western world. In Hegel's view, although at times philosophy's history seems to be a chaotic series of crisscrossing interpretations of meanings and values, with no consensus, there has been a teleological development and consistent progress in philosophy and philosophizing from the beginning; Hegel held that his own version of "German idealism" was simply bringing to final expression the latest refinements of an ongoing, perennial system.
If we take Hegel at his word, then one of the best entries into his system would be through the history of philosophy, showing how systems and schools of thought prior to Hegel led up to his system. The most important currents to focus on, however, would be in modern philosophy, in which especially intensive changes led ultimately to German idealism and Hegel's immediate predecessors.
Fortunately, Hegel lectured extensively on the history of modern philosophy and structured his lectures in such a way as to throw light on the status of the "one system" of Western philosophy at the time - the status to which Hegel felt he had been contributing and was continuing to contribute. These lectures are of interest, first of all, as a systematic chronicle of philosophical positions in the heyday of modern philosophy, from Bacon to Hegel. Second, they are interesting because Hegel's critical comments on his predecessors clarify his own positions: for example, the dialectic method and the importance of triplicity, the relationship of philosophy to the scientific method, the necessity for avoidance of the extremes of empiricism and of idealism, the subject/object problematic, the "identity" of rationality and reality, and the technical meaning in Hegel's philosophy of "absolute," "infinity," and the "idea."