Your question might get removed since really you are just polling users of this sub.

I work in the field of early Christian studies and have very good Greek and Latin, it's essential if you want to do serious historical research in Late Antiquity.

I only read Latin, unfortunately. I was initially planning to learn Greek as well, but I was distracted by seminars on archaeological theory and ended up going that direction instead.

My situation is sadly all too common among early medieval historians, who often know Latin but not Greek. This reflects a more general bias among medievalists toward the Latin west which, while being slowly corrected, remains very deeply established across the discipline. It's easier to find classes on Latin paleography (the study of ancient handwriting and manuscripts) than Greek, and some medieval studies departments require Latin paleography, but don't provide any support for Greek because the idea that you could be a medievalist who studies the Byzantine empire is still (strangely) so radical. But this is changing, and medievalists who do know and use both languages stand, I think, at an advantage for marketing themselves.

Among classical historians, classicists, and more propely Mediterranean late antique historians, however, it's normal and necessary to know both languages (though often to specialize in one more than the other). Many late antique historians will also learn Syriac, Coptic, and/or Arabic.

This is in addition to modern languages (French, German, etc), which all PhDs in medieval history (and most classicists, I believe?) are expected to know (my program requires proficiency in two modern languages + latin, which is typical for medievalists). Because of my studies, I also know a bit of Old English.

If you want to prepare for graduate studies, the most important thing you can do is start learning languages as early as you can. Reading is usually more important than speaking (aside of the University of KY, I don't know if anyone is currently teaching spoken Latin in America), and Latin is generally easier to learn first than Greek (I've been told). You should know at least Latin or Greek reasonably well, plus one modern language, before applying to grad school. If you can do more before you apply, your application will likely be more successful, because grad programs prefer to accept students who will not need to spend years learning languages before they can start reading their sources.

My experience in the UK is slightly different. I went into my Master's (in Late Antique and Byzantine Studies) with no knowledge of Latin or Greek, along with some incredibly shaky half-remembered French and German from school, but I was still admitted. The rest of my cohort are generally pretty bad at languages, especially the UK students - international students and those with a classicist background tend to know Latin and Greek already, as well as at least one modern language. After one year of admittedly pretty intense training in Latin and Greek, I was able to enter a PhD programme as well in the UK, so at least here it is possible to start grad school without any knowledge of ancient languages.