Well at your price range, you shouldn't have any difficulty building an absolutely fantastic machine.
To be honest though, you should include a new monitor into this build. They're only $130 and greatly improve the experience using your machine. I feel like it would be a travesty to pair a beast of a brand new machine with a 2002 monitor.
I've never had a media card reader that worked consistently so I just use USB ones. You'll have to pick one yourself.
ANTIVIRUS: Norton slows your computer down like crazy AND doesn't stop viruses pretty well. ADDITIONALLY, it costs you money. Save yourself a lot of trouble and get Avast! Antivirus Home. It's better and free. You do have to register it to an email address once a year, but that's a lot simpler than paying.
CPU: $315 i7-2600K
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115070&cm_re=i7_2600k-_-19-115-070-_-Product
Gaming only needs the i5-2500K for amazing performance. But other things like video work (and probably 3D Animation) can use the i7.
Cooler: $60 Tuniq Tower 120 Extreme
I can't find something that shows this heatsink ships with a socket 1155 mount (Sandy Bridge CPU socket). It comes with good thermal compound though (Tuniq TX-3). You only need an aftermarket cooler if you overclock. The Xigmatek Gaia (
http://www.newegg.com/Product/Product.aspx?Item=N82E16835233082&Tpk=Xigmatek%20Gaia ) is the best choice I know of for that followed by the Hyper 212+. But this one looks cooler and works great. Liquid cooling is either expensive and a lot of work to have a good working system or a gimmick (because cheap liquid cooling isn't really any better than good air cooling).
Mobo: $130 GIGABYTE GA-Z68A-D3H-B3
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128502
Since you're not a hardcore overclocker, this will do everything you want very well. You'll want Z68 since you're doing video work. It's got everything P67 or H67 has and costs the same as P67. If you think you might be more into overclocking, then drop $170 on this GIGABYTE GA-Z68X-UD3H-B3
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128498
RAM: $65 Kingston HyperX 8GB (2x4GB) 1600CL9
http://www.newegg.com/Product/Product.aspx?Item=N82E16820104173
Gaming only needs 4GB of RAM. With 3D Animation and video editing, you can use all the RAM you can get. Consider picking up another 8GB (2x4GB) kit of equal speed (MHz and latency) in a couple months as prices continue to drop. These two are also good
http://www.newegg.com/Product/Product.aspx?Item=N82E16820220558 http://www.newegg.com/Product/Product.aspx?Item=N82E16820220561
Graphics: $290 PNY GTX 570 w/ Lifetime Warranty
http://www.newegg.com/Product/Product.aspx?Item=N82E16814133370&cm_re=gtx_570-_-14-133-370-_-Product
A $200 GTX 560Ti would be amazing at gaming and adding a second would make your build max out any game two years from now (more or less). That said, your price range allows for excess.
HDD: $50 Samsung Spinpont F3 1TB
http://www.newegg.com/Product/Product.aspx?Item=N82E16822152185&Tpk=samsung%20spinpoint%20f3
Buy this RIGHT NOW because it's only this cheap once every couple months. Regardless of what you do with your computer, this is the fastest HDD out there and the one everyone will recommend anyways.
PSU: $85 Corsair TX750 V2
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139021
If you go with the GTX 560Ti, you can go with the $60 XFX
http://www.newegg.com/Product/Product.aspx?Item=N82E16817207014&cm_re=xfx_power_supply-_-17-207-014-_-Product
Do not cheap out on your PSU or you risk the safety of all your components! Stick to Antec, Corsair, Seasonic, and XFX unless you have an amazing stellar thorough review of another unit. Here's a typical bad unit:
http://www.jonnyguru.com/modules.php?name=NDReviews&file=print&reid=204
Case: $80 ENERMAX SPINEREX ECA5010M-B-B
http://www.newegg.com/Product/Product.aspx?Item=N82E16811124141
This is a personal preference thing--so you have to decide what you want. What matters most is air flow and appearance (so long as you're not getting a super cheap one so that build quality really matters). You also want a bottom mounted PSU.
DVD: $20 Any DVD-RW will do
Monitor: $140 22" LED
Newegg charges tax and recycling fees for monitors. If you live in somewhere like California, I suggest buying your monitor on Tiger Direct. All that really matters is you want an LED monitor given the choice of LED and LCD at similar prices. And 22" is the sweet spot, price wise.
SSD: $240 OCZ Vertex 3 120GB
http://www.newegg.com/Product/Product.aspx?Item=N82E16820227706&cm_re=ocz_vertex_3-_-20-227-706-_-Product
Install your operating system and specific programs that you want to be REALLY fast on this drive. There are other SSDs you can get, but nothing's as fast as the Vertex 3. If you want to save a couple bucks, the Agility 3 is great too.
OS: $100 Windows 7 Home Premium 64-bit OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16832116986&cm_re=windows_7-_-32-116-986-_-Product
TOTAL: $1575
You will also need SATA cables, thermal compound (I buy Tuniq TX-2 off of Amazon or ebay), and a Phillips (+) screwdriver.
You also have to check cooler clearance inside your case. Some larger coolers (like the Tuniq Tower 120 Extreme) won't fit in a lot of cases.
Do you care about blu-ray? That'll cost you $60 for a BD-RW on sale. Right now Blu-ray burning media is too expensive.
If you sign up for Newegg's email list, there will probably be some sales this weekend or next that will save you $100 total or so. I'd buy the HDD and case now though.