Can't really help budget wise (since I'm in the UK) but I've heard decent things about Lenovo and Sager. But if I'm honest with you my laptop knowledge is minimal. Keep an eye on this thread though, there will be a lot of troll posts since you're looking for a laptop, but there are some knowledgeable board members that are worth listening to.
You shouldn't be getting a laptop to play video games, you should be getting a laptop for your schoolwork. You're wasting all of that money on overpriced tech that could be better saved for a desktop. and no, laptops aren't truly portable, unless you count needing a cord hooked to your laptop for acceptable gameplay as "portable"
Yes sir, as I've stated already, I work a lot and this job I do requires me to travel. I insist on buying a decent laptop for both work and play. I NEED it for work, but the gaming part is for not boring myself to death. I have a decently capable desktop for gaming, but I don't get to use it much because I'm gone a lot. I miss playing games and I'm willing to "waste" my money on a laptop. I obviously have had laptops in the past, and I do know the difference between having my laptop run off battery and having it plugged in. It is still infinitely more portable than lugging around a desktop all over the place. I do not see this as a waste of money because it's what I want, and it's something I feel like spending my money I've earned on.
Don't pay him any mind he did the same to me and other people anytime a topic about laptops was posted. My budget is around the same so and I've been going here http://www.xoticpc.com/custom-gaming-laptops-notebooks-gaming-laptops-ct-118_96_98.html
Really good site you can choose the brand, processor and everything have fun dude and good luck :D