You don't need a laptop at all, usually. The school's computer lab will do you well 100% of the time if all you're looking to do is assignments.
However, if you're going to be moving out of town for Uni, and you won't have a desktop hanging around, then it's probably a good idea to get a laptop, simply for convenience's sake.
You can probably get what you're looking for at around ~600$, I don't know how much the extras would cost though, aside from the mic, which is pretty much standard in every laptop these days; they might only be present on higher-end laptops.
As for the gaming aspect of CS, it's unlikely you'll touch 3D stuff until your final year and even then, it's probably going to be fairly simple stuff that any regular graphics card'd be able to handle.
I'd strongly advise against getting Visual Studio if you're going to pay for it, because AFAIK it's relatively expensive (though I could be wrong on this, Microsoft does some good student deals, and your uni might have a deal to get you it for free), and there are plenty of good IDEs that don't cost a penny.
Tl;dr, to actually do your work, you'd honestly be fine going with a laptop from the year 2000, or even before, and using the open-source stuff that's free online. You really don't need a lot of power or money to do undergrad CS stuff.
