It's a very difficult task to reconstruct the way Hebrew was pronounced in ancient times. As you might know, the Hebrew alphabet is an abjad, which marks consonants in most of the cases, and the vowels have to be guessed using some help, called matres lectionis. Therefore linguists could reconstruct most consonants based on similar languages, and many rabbis from the Arab world used similar technique to figure out the meaning of some rare words. Another possibility is to use transliterations of Hebrew words in other languages (e.g. Ancient Greek, Latin), but one should be careful with this for obvious reasons. However, even in the era of the Talmud there were debates on different pronunciations (Megillah 24b).
On YouTube you can find many reconstructions. Almost exclusively they do the Tiberian Hebrew, which developed in the Land of Israel in the 8th–10th centuries CE. The reason is simple, the Masoretes tried to add some kind of notation of the vowels in order to preserve the reading tradition they had. There were other traditions as well, but the Tiberian one quickly became the standard among Jews.
This recording tries show how the Tiberians pronounced the consonants. In another video he tries to read a sample text. Here's another recording from 9:11. Please note that the vocals are mostly educated guesses. Rhymes, which are really helpful to determine the exact nature of vocals, were only used from medieval Jewish poetry. This reconstruction is very similar to the Yemenite tradition, since people from the Arab world can distinguish letters that most European can't. With the help of their geographical isolation, Yemenite Jews were very keen on preserving their own traditions, which were almost intact until their moving to Israel.
Regarding the cantillation part, it is a scientific dispute whether a single tradition existed. Some researchers maintain that there was one (e.g. Haik-Vantoura, Weil), while most of them (e.g. Avenary) refuse such possibility. Since there are different cantillation marks with the same grammatical function, it is quite sure that the Masoretes had a musical tradition to read the text, but musical notation was not advance enough in those years.