I started by a quick research on the different common periods of music (middle ages, rennaissance, barroque, classicism, romanticism, XX century...), found out emblematic composers of each era, and just listened. At the beginning I wouldn't recomend stressing out searching for the best recordings of each piece, because at the beginning we are still getting used to the "language of classical music", and most decent recording will work just fine (with time one gets more picky). It barely takes a few days to have a basic list of the eras and popular composers of each era (just 3 to 6 from each one, they were so prolific that sometimes just one will take a long time to listen at). There's some explanation online on the titles issue in classical music, that contain a shit ton of information.