Gaming Laptop? ($1k-$1.5k)

Save yourself the trouble of building a laptop. It's very difficult.

Building your own desktop will save you plenty of money, and also will be a great learning experience along with getting quality parts, if you choose to.

For your desktop
PCPartPicker part list: http://pcpartpicker.com/p/mQR7
Price breakdown by merchant: http://pcpartpicker.com/p/mQR7/by_merchant/
Benchmarks: http://pcpartpicker.com/p/mQR7/benchmarks/

CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($169.99 @ Microcenter)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.99 @ Newegg)
Motherboard: ASRock Z77 Pro3 ATX LGA1155 Motherboard ($94.99 @ Amazon)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($35.99 @ Newegg)
Storage: Western Digital Caviar Black 1TB 3.5" 7200RPM Internal Hard Drive ($96.00 @ B&H)
Video Card: Asus Radeon HD 7970 3GB Video Card ($352.00 @ NCIX US)
Case: NZXT Phantom 410 (White) ATX Mid Tower Case ($99.99 @ Amazon)
Power Supply: Corsair Professional 750W 80 PLUS Silver Certified ATX12V / EPS12V Power Supply ($109.99 @ NCIX US)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.99 @ Newegg)
Total: $1001.93
(Prices include shipping, taxes, and discounts when available.)

With that, you could get a cheap $500 laptop or something. As laptops are kind of big ripoffs, but this one is decent.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

IMO: I would get the desktop, then spend $500 on a apu laptop. You'll get the best bang for your buck there, as laptops are not the most reliable for gaming.

If you want a different case, you can tell me. I know many cases that would provide good airflow, at a reasonable price. Also stylish ones.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.newegg.com/Product/Product.aspx?Item=N82E168...