I've been an artist all my life and have been in the biz for at least 25 years now in some form.
I have two design degrees. One in Industrial design, the other in Graphic Design.
I would urge you to not only go for graphic design, but also marketing. Unless you plan on owning your own business, it's a very tough field to move up in if you just have a graphic design degree. Marketing opens up many more doors.
Also, I would say you need to be pretty well rounded in design. Meaning you can work in both the print and web mediums. However you may find that you are better suited towards one area and that is fine as well, just realize that you may miss some opportunities otherwise.
Get your BA or BFA first, but then if I were you, I'd consider a Masters as well.
It may cost you a lot to go to school, however in the long run it WILL pay off. Take the opportunity now while your young and have many years ahead of you to get as much education as you can. This will help in your career advancement.
Personally I waited until after I was out of the military to go to college. I didn't go for a Masters which I now regret and finding the time and money to do so now would be extremely difficult. So again, I'd urge you to do so now.
One big key to design is organizational skills. This goes much further then just slapping some graphics on a home page or printed piece. You need to be organized in you file maintenance, how you set up your files, etc. This should also translate to how you organize projects you work with as well as the clients you cater to, and any market research you do.
You can be a great and artful designer, but if you've got a messy desktop and/or can't keep files, clients and other work related stuff organized and easy to find, then you will do yourself a great disservice as well as your employer and may find yourself out of work. So PLEASE keep that in mind.
Also, while having a full-time job pays the bills in many instances, don't allow that to be your only option for making money. Many designers also work freelance. That is to say not "FREE" but rather working outside of the office setting. For instance having a room in your home dedicated to your profession. (A home office)
With that you generally have more freedoms with design and other than the client won't have others looking over your shoulder to tell you how to design (and/or steal your ideas-which happens all to often). Freelance can be lucrative, but at the beginning, do not expect to make a bundle from it. It's generally those long term designers who have built up working relationships with their clients over the years who have the network in place to support a thriving freelance business.
One last thing, if you get involved in the print side of things, make sure you learn about PRE-PRESS. Whether you are in business for yourself or work for someone else, knowing how to correctly set-up files so that there is NO problem when sending them to a print shop is a great advantage. This will save either yourself or your employer time and money. Check your learning institution to see if the offer any classes for pre-press. It's not often a college does, but if they do, be sure to take what they offer in that area (again should you decide to work in the print design industry).
If you have ANY questions, please feel free to PM me.
Not only do I have the degrees, but have worked in the business for 25 years. As well, I've been a designer, pre-press/production artist, supervisor and art-director. I should be able to answer just about any graphic design related question you have.
One final piece of advice, while in school, treat it as your JOB. If you don't do well at your job you'll get fired. In this case if you don't do well at your job (college) you won't get good grades and have to retake classes costing you valuable time and money. I'm not saying to not have fun while in college, just be responsible with it. Don't party too much or you may live to regret it for the rest of your life. Study hard now so that in the future you can live a more comfortable life. There is plenty of time after college to have fun, just in a different setting.