CHALLENGE: Can you buildapcforme that is a better value / more suited for my family than the i3 Alienware Alpha

A bit more expensive, but will absolutely destroy the Alienware.

PCPartPicker part list / Price breakdown by merchant

Type Item Price
CPU Intel Core i3-4150 3.5GHz Dual-Core Processor $104.88 @ OutletPC
Motherboard MSI H81M-P33 Micro ATX LGA1150 Motherboard $44.88 @ OutletPC
Memory G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory $62.99 @ Newegg
Storage Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive $48.88 @ OutletPC
Video Card Sapphire Radeon R9 270 2GB Dual-X Video Card $136.99 @ Newegg
Case NZXT Source 210 (Black) ATX Mid Tower Case $29.98 @ OutletPC
Power Supply EVGA 400W ATX Power Supply $9.99 @ NCIX US
Operating System Microsoft Windows 8.1 (OEM) (64-bit) $87.75 @ OutletPC
Total
Prices include shipping, taxes, and discounts when available $526.34
Generated by PCPartPicker 2015-01-25 12:07 EST-0500

Closer to your maximum budget, will be ~2x as powerful for AAA gaming as the cheaper build above and will absolutely annihilate the Alienware.

PCPartPicker part list / Price breakdown by merchant

Type Item Price
CPU Intel Core i3-4150 3.5GHz Dual-Core Processor $104.88 @ OutletPC
Motherboard MSI H81M-P33 Micro ATX LGA1150 Motherboard $44.88 @ OutletPC
Memory G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory $62.99 @ Newegg
Storage Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive $48.88 @ OutletPC
Video Card Asus Radeon R9 290 4GB DirectCU II Video Card $239.70 @ Newegg
Case NZXT Source 210 (Black) ATX Mid Tower Case $29.98 @ OutletPC
Power Supply EVGA 400W ATX Power Supply $9.99 @ NCIX US
Operating System Microsoft Windows 8.1 (OEM) (64-bit) $87.75 @ OutletPC
Total
Prices include shipping, taxes, and discounts when available $629.05
Generated by PCPartPicker 2015-01-25 12:09 EST-0500
/r/buildapcforme Thread