In my opinion HP is not a brand you can trust to be good.
I have myself a MSI GT780DX notebook and im quite happy with its performance (even the warranty repair was great as in Poland, returning the Laptop fully fixed in under 1 week, but dont know if thats how fast they operate worldwide).
For the money you mention id probably either try to aim a Samsung gaming laptop, MSI or asus. Eventually Toshiba.
Apart from that, its a bit hard to advice you withouth more information. You should fill up the questions in the forum to give us as much feedback as possible.
Some advice AVOID Dell, sent my laptop in about 10 times or so easily and majority of the they never fixed the problem. And their customer support is horrible, I can go on about them for quite a long time. Not to mention they couldn't even design the laptop properly so my model had a problem with heating up and causing hardware issues concerning the power connection over time, and this was not isolated with just me but with a large chunk of the people who owned one. So yeah in short avoid them.
For gaming laptops one of the things you need to look at which isn't usually apparent is how it is cooled, the CPU/GPU throws off a lot of heat and the way laptops are designed aren't very effecient in disipating it so take note of how it disipates heat. It is one of those things you don't care about untill you have problems with it and when you do it's a bad day. Also spray a can of compressed air into the airvent to blow out dust build up every now and than.
In terms of build materials keep in mind plastic keeps heat in and doesn't disipate it. Where as aluminum will actually disipate the heat helping keep the laptop cooler.
Just some things I learned from my laptop, hopefully it helps.