Select a programme with a strong foundation in data structures and algorithms, theoretic computer science, linear algebra and at least a few more semesters of mathematics, some basic digital circuits and microcontrollers, assembly languages, parallel algorithms, networking. Basic Newtonian physics, probability theory, statistics or relational databases aren't a mistake either. These will lay out some computer science minimum for you. Then you need to get into C++ (asap) and as many other languages as possible, gradually, so you aren't scared of anything. As for (advanced) computer graphics, that's a topic for masters, I believe. If you'll hear terms like rendering equation, BRDF, BVH, kDtree, path-tracing, Monte-Carlo, convex hull, ... that's what's going to be in a master's degree (not viable without the few semesters of mathematics). This is about what I got (2004) and it made me aware of all the different stuff I might have and you bet most of us have encountered to some degree.
Over the years I also managed to forget most of the details... But I know where to look and what do the things "do".
Regarding C++, DirectX, OpenGL, shading languages, assembly languages, networking, gameplay scripting, Unity, Unreal, Maya, 3dsmax etc, they showed us a lot in school but they'll never show you enough, they can't and it isn't their goal. Work at home, make (little bullshit) games at home, create a small app to help your mother sort books in her archive, make an app to count beers in the pub, clone asteroids, mario and tetris, write your own UDP chat application... WHATEVER is going to help you.
I ended up doing engine/render in an AAA company and if you send us your resume and we see you graduated a computer science / software engineering programme, it's a big plus. Then if you show us that you made this small thing here and that funky thing there, it's going to sound even better. It's going to sound very good for an engine coder, for a gameplay coder you'll have to show even more of your own games, but the CS basics are going to be important as well. In either case and coding role, expect basic CS/algebra/C++ tests when applying to gaming companies, to filter out people without even minimal knowledge.
Good luck!
Off-topic: "Online" university sounds weird, maybe I'm old I think I'd miss shaking in the cold, dark and hundreds of years old hallways with a bunch of schoolmates before and after any harder exam... plus the exchange programmes (at least in EU) But I understand it's becoming an option nowadays.