So I would focus on those classes that get you the skills to do this. Such as video production, web design, etc. For your BA major think strategically long term. Where do you see yourself 20 years from now? Way past the entry level job? At an agency? Running your own agency? Doing something creative? There are a lot niches in advertising world from account management, to finance, producing, planning, creative, etc. Use your college education to become the person who sees the bigger picture and can manage all aspects from account management, strategy, analysis of data and trends, the design and execution of creative, including where it is placed. This is the longterm goal.
To answer your question about social media. One of the best guys out there doing it now with his own large agency is Gary Vaynerchuk. He says all the time social media is always changing and he always looking at which platform is gathering an audience and the attention of people. Because it is always changing I would say go intern and hopefully work for people like him. Work on finding the niche that you enjoy and become the best at it.
Another idea is to find small businesses and nonprofits that need social media management to cut tour teeth and learn on. This you could do while studying.
Also watch that college debt. Saleries starting out and mid level may not be so great.
I think most large companies will want a realated degree as a standard, but really not sure it matters over span of a career in this field what it is. If you can come to the table starting out with practical experience growing sales in social media space, that’s what they want. Business people I deal with want me to bring them customers.