This is why why I wanted you to fill out the form. Otherwise we would have given you a gaming rig like you said in the OP, but it wont be able to video edit.
Monitor: ASUS VE248H 24in. $195
http://www.pccasegear.com/index.php?main_page=product_info&cPath=558_1212&products_id=16558
Standard TN panel, 1080p 60hz monitor with 100mm VESA mounting. Fairly standard monitor.
CPU: Intel Core i7-3770k. $335
http://www.pccasegear.com/index.php?main_page=product_info&cPath=187_346_1184&products_id=20140
Strongest chip your going to get on the mainstream platform and is overclockable. Should be plenty for your needs.
CPU Cooler: Coolermaster Hyper 212 EVO. $35
http://www.pccasegear.com/index.php?main_page=product_info&cPath=207_23_845&products_id=18670
The go-to budget cooling option, will support a moderate overclock on that 3770k (wouldn't go further than 4.4ghz on it).
Motherboard: AsRock Z77 Extreme4. $139
http://www.pccasegear.com/index.php?main_page=product_info&cPath=138_711_1183&products_id=19867
While this is a more budget end enthusiast board, it will do everything you could want. Has near all the features of much more expensive boards.
RAM: G.Skill Ares 16GB (2x8GB) 1600Mhz CL9 1.5v. $82
http://www.pccasegear.com/index.php?main_page=product_info&cPath=186_912&products_id=19766
16GB of fairly standard RAM, Low Profile so it wont conflict with large CPU heatsinks.
PSU: Silverstone Strider Plus 750W, 80+ Silver Fully modular. $145
http://www.pccasegear.com/index.php?main_page=product_info&cPath=15_995&products_id=15350
Very good unit, have this one personally and love the thing. Very good reviews and not as expensive as a similar Corsair unit.
GPU: Gigabyte HD7970 Ghz. $469
http://www.pccasegear.com/index.php?main_page=product_info&cPath=193_1309&products_id=20995
Just about the strongest single GPU on the market, should also come with some free games. Make sure to ask about that when you order it.
HDD: Seagate Barracuda 2TB 7200RPM. $99
http://www.pccasegear.com/index.php?main_page=product_info&cPath=210_344&products_id=19554
SSD: Samsung 830 128GB. $95
http://www.pccasegear.com/index.php?main_page=product_info&cPath=210_902_1370&products_id=20429
Case: Coolermaster HAF-X. $189
http://www.pccasegear.com/index.php?main_page=product_info&cPath=25_31&products_id=14840
Bit overkill, but I can hardly say anything since I have one under my desk right now for a much lesser rig. Very future proof this case, will support just about anything you throw at it.
OS: Windows 7 Home Premium 64bit or Win 8 64bit OEM. $95 or $99
http://www.pccasegear.com/index.php?main_page=product_info&cPath=375_974&products_id=21773
http://www.pccasegear.com/index.php?main_page=product_info&cPath=375_974&products_id=17003
Total (Win8): $1882
Well under budget and will play games at max settings and edit/render videos very nicely.
If you really want to spend more money, dont bother with the main components, they are already plenty for your needs and to get stronger hardware will be redundant.
Places I can see you sinking money into and having a good effect is a bigger SSD, another monitor (maybe two more, video editing across multiple monitors is so much better, believe me) or even a custom watercooling kit. If you were willing to go over-budget, you could get three monitors and another HD7970 and get yourself a really good Eyefinity setup.