If I could do it over again, I wouldn't go into graphic design. That's only my two cents worth because I didn't have the stamina and self discipline to study outside of class enough - and you HAVE to practice, practice, practice a lot if you're new to it (and I was).
Also, there really is no such thing as web design, in my opinion. There are web producers and programmers. And if you want to make websites, you better be good at programming because no one wants a simple site - they all want content management systems; i.e., blogs, e-commerce and forums.
I'm really not trying to be negative. If I could do it over, I might even do it the same. But I sure would have studied Adobe products and graphic design much earlier than I did. I tried learning it all at 42 and it's taken 5 years to get average/above average. I want to excel, of course.