Late Classical heading into Medieval and even Renaissance for me is usually defined by what wonders I want, since the competition is much stronger and many of the earlier wonders have game-defining utility. The big ones to me are Oracle, Great Wall, and Colossus in late Classical, and also University of Sankore, and the various religious wonders.
Typically:
Tradition start - University of Sankore then Leaning Tower, that combo typically allows any Tradition civ to slam-dunk the competition, bonus points if you got Oracle on the way. Sometimes I have to delay the rush to some degree here or there depending on culture output.
Progress - rush up to Banking, hopefully picking up Forbidden Palace along the way. This gives you a ton of the gold buildings and over time you'll build up a lot of buildings that need to be built as you backfill, and you can now get some science at the same time. It is also nice that since this one ends in a non-wonder you can't get screwed by policy number.
Authority - get Knights, kill everything. If you are planning to continue warmongering you just rush up for more military techs, if you have a peaceful transition point head for that, Banks are still a solid choice to backfill all that infrastructure you probably ignored.
Religious considerations - the religious wonders are huge game-changers as well if you can't spread (St Basil) or if you plan to ultra-spread (the others).
Final notes, if I am pretty sure I'll miss some of these wonders I'll try to adjust to pick up others so I don't just give up everything for free.
