If you are going to play a lot of demanding games, go with Intel for sure. For graphic cards it's up to you ... i have a 1200$ budget and i went with a GTX 660Ti because it was on sale and because it's pretty good card for the price. For that budget, i wouldn't be going with a SSD but it depends on you. Here's a system that may suit your needs :
CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($189.99 @ Microcenter)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.99 @ Newegg)
Motherboard: ASRock Z77 Extreme3 ATX LGA1155 Motherboard ($109.99 @ Newegg)
Memory: Mushkin Silverline 8GB (2 x 4GB) DDR3-1600 Memory ($36.99 @ Newegg)
Storage: A-Data Premier Pro SP900 64GB 2.5" Solid State Disk ($59.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($69.99 @ NCIX US)
Video Card: Asus GeForce GTX 660 Ti 2GB Video Card ($295.99 @ SuperBiiz)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($49.49 @ SuperBiiz)
Power Supply: SeaSonic S12II 620W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($78.99 @ SuperBiiz)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.89 @ Outlet PC)
Total: $949.30
(Prices include shipping, taxes, and discounts when available.)
Wireless is not integrated in the motherboard but you can buy a PCI wireless adapter :
http://www.newegg.ca/Product/Product.aspx?Item=N82E16833166011 (14.99$ @ Newegg )
All that stuff fits your budget and is good quality .... Computer case is only only a personnal choice because it's good and look great.
Hope it helps