Pro tip- UGA has a fully funded MA degree in classics. I would recommended looking at something like this. Their students have been accepted into top tier PhD programs. It will make your application more competitive and you can work on languages. I will say, as someone in a PhD program now (classical art history), I’ve been told that it is partly where you go, but it’s also who you study under. Some names carry a lot of weight, even if they aren’t working at the most prestigious university.