I was confused by the part where you said "I don't know specifically what I want to do as a career."
Yes, a portfolio website is important for a game programmer -- but not until you have something to put on it.
Making a website is a lot like programming. When you are ready to make one, you can easily learn how to do it. That bridge is still far away.
Likely my fault for not clarifying that in the OP, my apologies.
Alright, thanks for the advice regarding that.