I would like to play on these settings.
Preferred Minecraft settings: Fast, 12 chunks, V Sync off, would like stable 50-60 FPS (I have Optifine installed)
Preferred GMOD settings: Medium to High, would like a stable 50-60 FPS
Preferred Day Z settings: Medium to High, would like a stable 40-50 FPS
The most basic "gaming" laptops start at $750. An okay one costs $1k, a good one $1250, and a great one $1500+
For your budget you should choose a desktop instead. You'll get the performance you want for your budget.
I think the best game supporter is 1.73 GHz Processor, 2 GB Ram, 80 GB Hard drive. As you require. An external graphics card enabled powerful Graphics Technology.