My personal opinion is to get a broad degree that's affordable. Easier said than done for some disciplines. A lot of the game colleges are “for profit” and cost a ton. I got a computer science degree from a state school and now work as a programmer at a AAA game studio. A lot of people get burned out in the gaming industry due to crunch and long hours. So having a degree that can be applied to other fields is useful if you need to get out of the industry. That's just my opinion though.
Also the gaming industry isn't the best paying industry either (it isn't bad, just isn't the most $$ you can make out of college). So paying off big loans can be a challenge. For an entry level job, the same degree can be 10k less per year (at least for programmers). I know this from experience ?
That being said, a lot of people who I work with went to places like fullsail, digipen, scad, guildhall, and many other game oriented schools. Not all though, some had a similar path as me. The one thing I hear in common about those game programs is “you get what you put in”.
My company cared much more about my portfolio and the skills I had than my degree title.
Use your first year in college to explore some majors. Programming isn't for everyone. Neither is art. To really make an informed decision for your self, you should probably test the waters of programming(ue4/blender), 3D modeling(blender), etc.