yea, for what I have read, dante didn't read that many greeks, but he was strongly influenced by aquinas, which had as main study topic aristotle. so sure, studying aristotle is very important, not to understand dante, but to understand aquinas and consequently dante.
user, you don't have to read every single book from homer to dante, thats impossible. read the most important works and/or works that interest you.
my recommendation: read the divine comedy now. seriously. don't wait until you have read all books in your list, read it now.
Divine comedy was the first Veeky Forums book I read, I had no philosophy, literature, theology or historical background, seriously, I didn't know who odysseus was. Still, I enjoyed it a lot and it inspired me (almost forced me) to start reading literature and philosophy seriously, and now, couple years later, I am re-reading after reading homer, hesiod, the greek playwrights, joyce, the bible, and it is magnificent. its very nice to re-read a work after some time, you will be able to notice how much you evolved since you read it
, you will get much more references and will get more out of it
and yea, I am still finishing the greek playwrights, next I will read herodotus and thucydides, then some greek mathematicians like euclid, apollonius, archimedes and nichomachus to finally make it to plato and aristotle, so tldr, I am reading it the second time not even half-way throught the greeks, and I am being able to enjoy it a lot. don't wait months/years to read something you would like to read now, that you discourage you and you might give up
plus, its always important to re-read books, specially one like divine comedy, so read it now, the next time you read it with more background, you will get even more out of it