Build a PC and buy a cheap laptop.
- You really should be studying at college, not gaming. While some people can control their desire to play games, others cannot. I had two friends drop out of college - they gamed so much they failed enough classes making they were kicked out of school. And my undergrad school was no slouch (a quarter of the class were high school valedictorians). So they were more than capable of passing the classes, they just couldn't stop gaming. By getting a cheap non-gaming laptop, if you find you have problems limiting your gaming, you can take the laptop and go to the library or lounge to force yourself to get schoolwork done on a computer without the temptation of firing up a game.
- As mentioned, gaming laptops are a poor compromise. I see them as more for traveling, where you want to limit the amount of weight you're carrying around. That's not an issue in college since you can leave a beefy desktop in your dorm room. You will want a laptop with at least 6+ hours battery life to get you through a day of classes, and that pretty much excludes every gaming laptop.
- If you do want to game on the laptop from your bed or the sofa, you can always use something like Steam In Home Streaming to play the game on the desktop, but stream it to the laptop. To the laptop, this is no different than streaming a movie, so battery life is minimally impacted.
That said, you do need a way to relax and unwind from the stress and pressure of your classes. If you like gaming, then that's an excellent way to do it. Just be careful to make sure you're in control of it, rather than letting it control you.
CS is really more about algorithms and theory than it is programming. If you're taking a programming course, you'll need a computer. But most CS courses could actually be done without a computer. I would look at the syllabus for required classes for your major, and see how important the computer will be. Personally, I find a second monitor to be the most important thing for programming. There is no way i'd want to do it on just a laptop screen.
Also, do not get the WD Blue HDD, at least not unless you're also going to have a SSD. The WD Green and Blue drives have a head parking issue which can cause stuttering in games. I had assumed only the 5400 RPM drives were affected, but someone with a 7200 RPM WD Blue drive reported a similar problem earlier this year. Unfortunately he didn't report back if the fix I sent him worked, so I still have no confirmation if the 7200 RPM WD Blue drives are also affected. But better safe than sorry. The Seagate, Toshiba, and WD Black HDDs are fine (in as much as HDDs are fine as system drives).