Get a Mac.
Jk! Only if you want. Most people reject it out of hand because its more expensive, has a different operating system and/or they don’t like the Aluminium Unibody design. I only wanted to suggest it because I personally like it, and you might too. Or not. Either way, just putting it out there. If all you want to do is play Minecraft and Source games, then you can do that all natively; the new MBP range should be able to do it pretty well (from what I can see from the specs).
You might also be able to get an academic discount, which makes the hardware a bit cheaper (and the software, but that goes for Windows too), but above all else; don’t shoot the messenger.
Moving back to PCs, I can’t comment too much on the specs of the machines currently on the market, only since I’ve been out of the marketplace for a few years and haven’t been keeping up to date. I can only say that I’ve had superb experiences with HP in terms of service, even when longevity was in serious question. IBM and Toshibas are higher end and will have better longevity, but at a (massive) cost.
I think one aspect you should consider that you may not have is that of weight; one advantage that the ultra-portable ranges of laptops have is that they literally weigh nothing in comparison to other laptops. Carrying around a 5kg behemoth gets old really fast, but weight comes at a premium, either in terms of specs or cost. So consider the fact that, as you are going to be using this for school, you will likely need to lug it around quite a lot, and keeping the weight down to around 2kg is probably optimal. My Macbook (for comparison) weighs exactly 2kg, and my old HP 6910p weighs about 2.5kg, and I’d say that’s even erring on the heavy side.
Bear in mind that making a good investment now will probably keep you set for 3 years, but that an unwise one may only last 6 months. Getting a laptop that you hate and is entirely unsuitable for your needs is a complete waste, and so even if you end up paying a few extra hundred dollars to get the machine that actually suits your needs is the best option you can pick.