smorizio provides solid advice. Pay attention particularly to the PSU bit; a dodgy one can take out a whole system easy. You're much better off buying a PSU from a reputable brand such as Corsair, XFX or Seasonic.
You're going to be gaming, yeah? So no i7's; i5s will more than suffice. I chose SB simply because it's perfectly fine for gaming. It would be a different story if you were doing something other than gaming or had more money to work with. I picked a Z77 board to let you have the option of going for IB if you really wanted to.
Even though you don't know how to OC yet (I'm assuming), it's easy to do it with the SB series. Stock cooler will be fine on mild OCs. Emphasis on mild. If the budget permits you can get an aftermarket cooler down the road, namely the Coolermaster Hyper 212+ EVO; cheap and sweet.
The case would ideally have good airflow, but if you would like a silent build then let us know.
RAM is 8 GB since it's so cheap nowadays. But if you're looking to cut a bit here and there then downgrading to 4 GB is fine.
PSU I picked from Corsair since they've always been known to be very reliable, which is one of the main things you're looking for in a PSU.
SSD is a luxury, tbh, so if you really need some extra cash cutting it off is ok, I suppose. But a big part of the speed of this build comes from it, so think about it a bit first before dropping it.
Oh and for DVD readers any OEM unit from LG or Sony will do the trick for around $20. Blu-Ray capability will, of course, cost you a bit more.
CPU: Intel i5 2500K - $219.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115072
MOBO: ASRock Z77 Extreme4 LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard - $114.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157293
GPU: HIS H785F2G2M Radeon HD 7850 2GB 256-bit GDDR5 PCI Express 3.0 x16 HDCP Ready CrossFireX Support Video Card - $249.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16814161406
RAM: G.SKILL Ripjaws X Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model F3-12800CL9D-8GBXL - $45.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231428
PSU: CORSAIR Enthusiast Series TX650 V2 650W ATX12V v2.31/ EPS12V v2.92 80 PLUS BRONZE Certified Active PFC High Performance Power Supply - $89.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139020
CASE: COOLER MASTER HAF 912 RC-912-KKN1 Black SECC/ ABS Plastic ATX Mid Tower Computer Case - $59.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119233
HDD: Western Digital Caviar Blue WD5000AAKX 500GB 7200 RPM 16MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive - $69.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136769
SSD: Crucial M4 CT128M4SSD1 2.5" 128GB SATA III MLC 7mm Internal Solid State Drive (SSD) - $89.99
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&N=100006670&isNodeId=1&Description=M4&x=0&y=0
TOTAL: $941
That leaves you $59 to play around with the peripherals of your choice. But I'm sure you can extend your budget slightly by around $70 to get:
RAZER DeathAdder Black 5 Buttons 1 x Wheel USB Wired Precision Optical Gaming Mouse - 3.5G Infrared Sensor - $49.99
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&N=100006670&isNodeId=1&Description=deathadder&x=0&y=0
Logitech G110 Black USB Wired LED Backlighting Gaming Keyboard - $69.99
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&N=100006670&isNodeId=1&Description=g110&x=0&y=0
Hope that helps you. Of course everything is your choice, especially on items that are very subject to personal preferences, such as the case. I just chose what I would like on a rig for ~$1000. You are overbudget by a bit though, so I'm hoping you're a student so you can get the OS for the cheap. Otherwise...
And a final word; when asking for build advice next time, answer the questions I posed to you in the OP. That way we can answer you that much faster. You're doing yourself a favour, really
Happy spending