I'm not entirely sure what it is you mean by the first three sentences, but your question is: should you take Latin, Greek, or another class. The answer is that you should take what you want to take, provided that any of the options will suffice for your degree. If you are interested in European history beyond the ancient world, then by all means go do that! Are you afraid that Churchill's ghost is going to come reprimand you for not learning Latin? :-)

I really don't have a dog in this fight, being neither a classics major nor a student of Greek and Latin, but this seems a bit peculiar. Does your university really allow a student to graduate with a classics degree without taking either Greek or Latin? I know that was not the case when I was in school - the classics people had to take something like eighteen hours of languages. Is this modern English history class an elective? I can't imagine how it would count towards your major requirements - classics is, well, focused on the classical world. Take it from a guy who took seven years to graduate: if in doubt, pester your adviser.