Since no one else is going to suggest it: CHROMEBOOK~ (I am the super bias, but let me talk anyway.
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I agree with BasicAcid - if you want something for gaming, your best bet is get a PC. In fact, if you know what you're doing, you can build a PC at the console price that still performs just as well as the consoles, then it's just a matter of improving it as you get the money. However, if you were to get a Chromebook (most sell for ~$200-300 to memory), you'd have plenty of money to still spend lots on that perfect gaming PC.
Now, I know what you're going to say - "but it's useless if you don't have an internet connection..."
EXCEPT, if you're getting it for uni work, you'll rarely find a situation where you won't be with wifi anyway. And if you DO use it whilst travelling, you can still get access to basic writing/presentation/spreadsheet programs for offline use, and so can do assignments on the train. I even found a notepad app that I can use to write up LaTeX assignments on the way to/from uni. The Chromebook is also super light and portable - it's been everything I wanted and more for my time at uni.
FINALLY, you could still use it to play games at home/use windows software. All you need to do is activate remote desktop on both your chromebook and home PC (pretty easy to do), and you can then use your Chromebook to use programs on your PC at home as long as both are connected to a source of wifi. This means that you can still use your Chromebook for gaming.