Study C.S. and do indie games development in your spare time. XNA is pretty easy to get going. You might even be able to make a game for your final year project.
One day the games industry will spit you out, and you'll be looking for another job. At that point you might think "Hey, maybe there's more money outside of games" and start looking for other programming jobs.
If you've got a "Video Games" degree, employers will take one look at your CV and think "plays games all day. No use to us, we need serious engineers".
Games programming is very hard, but most employers (or agencies / HR people) don't seem to grasp that.
Also there's a fair number of Video Games courses that are pretty useless too - as someone who's been involved in interviewing people for games industry programming jobs, I can say the ones with CS experience often have a far better grounding. Having some solid demos that show your coding ability is far more valuable.