I wouldn't worry so much about how much you need to know to be good. Sometimes you need to know something enough to get a job done which is how I think of Python. Reality is python is a general purpose language, it's useful in about a million different ways and it's really not a difficult language. Everyone should have python in their toolbox. So just start using python. Use it for fun little projects that aren't necessarily school work. C++ is probably going to be the more difficult of the two. C++ is what you'll want to do when you are writing anything that needs to be really fast.

I'd take the classes in C++ and teach myself python through fun projects

Someone who is a skilled with C++ is an asset and often a useful and desirable part of a research or implementation team.