Here I address not the historian and scholar of the Hellenistic world, but instead I address the person who is trained in modern astrology and comes to the ancient Hellensitic astrological tradition for the first time.
There are several issues that one who is familiar with other astrological traditions must confront immediately. For some people, it would be easier to learn Vedic or Chinese astrology, which appears sufficiently different from custom to require any adjustments. Here are a few:
No Outer Planets: all of a sudden the natal chart looks more barren and appears to give much less information. This means that we have to find more information from the visible planets than we are used to finding. There is one consolation: Hellenistic astrology uses some additional positions in the birth chart: fixes stars and lots. The natal chart will not seem so barren for long.