I would study whichever languages you are more interested in. If you want to do advanced work in linguistics, think carefully about what sort of research you'd like to do. If I were you, I'd study Chinese because I'm come to appreciate the usefulness of spoken languages, but to each her own.
Since you're looking forward to a classroom where people are speaking ancient Greek "all the time," I'm sorry to say you'll be disappointed. Unless your professor is incredibly eccentric, you'll hear virtually no Greek spoken--just shaky recitations of whatever texts you're studying. Same with Latin (although perhaps less shaky with the pronunciation).
Horae quidem cedunt et dies et menses et anni, nec praeteritum tempus umquam revertitur nec quid sequatur sciri potest. Quod cuique temporis ad vivendum datur, eo debet esse contentus. --Cicero, De Senectute