As Greece, Bee-lining Political Philosophy----> Medieval Faires and then picking up what you need sounds incredibly strong. By the time you get Medieval Faires and the 100% adjacency bonus for theaters your Acropoli's should be pretty much up and running...and let the culture snowball begin
I don't know about bee-lining for Medieval Faires. Since the culture victory condition is again based on tourism, it doesn't seem to matter that much to be able generate very much culture early. I'm thinking it would be more important to shore up the GPP generation, because having a lot of great works will be the key to victory.
Political Philosophy is really great to beeline though. Start building up Classical Republic's legacy bonus to GPP, and use Charismatic Leader to start building up envoys.
What I'm wondering about right now is whether to grab the religion or not. As Greece, you can run both Urban Planning and God King, so early pantheon is a given. You can also research Mysticism early and be the only one who can use Revelation policy (+2 Great Prophet point) then and there. So that's a guaranteed first religion, second if someone else built the Oracle.
Having an early religion seems good because some of the beliefs are great for culture victory. Cathedral (1 slot for religious art) can start the tourism game really early. World Church (+1 culture for every 5 followers of this Religion in other civilizations) is potentially broken here, if we manage to convert a bunch of enemies and city states.
So this is definitely doable if we want to do it. But, I wonder that's the way to go. This would obviously require a fairly heavy investment in the early game, and moderately throughout the game. It would require us to build a holy site first. Then we need to spend a significant amount of faith spreading the religion and unlocking beliefs, etc.
I wonder if it would be better to just abandon the religion route. Go very expansionist at the beginning, perhaps even clear nearby civ for space using the hoplites. Having more cities means more acropolis, which is always a good thing. Then throughout the game, only spend faith on Great Writer/Artist/Musician.