Yeah, if you want to run games well on a laptop you need to buy one with a dedicated graphics card, RAM will only increase boot times and speed overall, not your game graphics.
MC at 16x16 is not hard to run and not as GPU intensive as other games. Under 500 is a very tight budget to play those titles. I suggest saving some more money and buying a PC in the 600-800 range.
If you want a gaming laptop, you shouldn't purchase one for less than about $1000. A desktop is much more reasonable, and a better choice.
Agreed, a desktop will serve you much longer as you can easily upgrade almost anything in it. If you are at a budget and you want to play Black Ops 2, as much as it pains me you should buy a PS4 or a Xbox One. :/
I completely spaced on you, sorry. Here's what I use to get a basic idea of a build: http://www.logicalincrements.com/, Just find the tier that fits your budget and then look up the parts. I would highly recommend building your own vs a prebuit, you'll loose a large amount of performance if you buy it prebuilt.