tbh youll get a laptop for that price, admittedly itll be either a low end dell (if you include your keyboard budget, which is gonna set you back another hundred if you want a bluetooth one) or second hand, but neither are hge problems if its only for typing.
What exact use are you going in for? A lot of comp sci guys i know spend inordinate amounts of time in the clusters at uni anyway, and i assume you have a half decent desktop? If you do youre set, forget about taking notes on one, itll last about a week, if that, and goes out the window as soon as you need to draw anything or write down a formula (would have thought games courses would include fairly decent amounts of mechanics, vector calc + fluid dynamics.)