For $1000, the gaming and video editing capabilities of this PC are quite hard to beat. This PC is very capable of editing 4K video footage, as well as gaming at 1440p.
On the CPU side of things, I chose the Intel Xeon E3-1231 V3. This 4 core processor also packs 8 threads, making it essentially an Intel i7 processor at a much lower cost of only $250. While it might not be overclockable, this thing still packs a punch in games due to Intel's excellent single-core performance. Screw you AMD, Intel rules at this price point! For some extra money, you can go with a Xeon with a higher core/thread count if you need that, or an i7-4790K/5820K/4960X/6700K if you want overclockability (Although you will have to get a different motherboard and RAM). This Xeon will be cooled by the Cryorig M9i, which is on-par with the popular Hyper 212 EVO for 2/3 of the price.
This Asus H97-Plus mobo is a very high quality H97 mobo that doesn't break the bank. It has great features, more than we need actually, and should last a very long time. A Z97 mobo isn't needed, because you won't be overclocking this Xeon.
The RAM I chose out is a 2x8GB kit from G.Skill clocked at 1866 mhz. This is a high-quality, high-capacity kit that should fulfill your gaming needs, and (hopefully) editing needs as well. You can buy the same kit later on if you need a grand-total of 32GB of RAM, but for most people that still won't be necessary, as 16GB is usually enough.
On the storage side of things, a 240GB PNY CS1311 SSD will be your boot drive so your computer can boot up quickly, and its extra speed will also help you a lot when exporting and importing video. A 2TB Seagate Barracuda drive will store more unimportant programs and files, and as long as you correctly manage your video files and (hopefully) store a lot of your projects elsewhere, this 2TB drive should be enough. No worries, as this PC can handle several more drives being put to use.
The graphics card I chose out here is the GTX 970 with an EVGA cooler slapped on it. This card will max out games at 1080p, and provide respectable performance at 1440p. Additionally, it will work hard as you edit, and CUDA acceleration will definitely help you out if you use it. Otherwise, you might want to go with an AMD option if you prefer, such as the R9 390.
For the case, I chose out the very popular and very great NZXT S340. It has a beautiful window, good cable management, and awesome reviews. We need a beautiful case for a beautiful computer, after all.
Here we have a high-quality 650W 80+ Gold unit from EVGA, featuring semi-modularity. This PSU handles all of our components efficiently, meaning you won't pay as much on your electricity bills, and it also has a high-enough wattage rating to handle even a 980 Ti if you choose to upgrade to that!
Other Things You Might Want To Get
External Blu Ray/Optical Drive: You should probably already have this if you need it... but get one if you don't have one and you do need it! Wifi Card/Adapter: Ethernet is usually/always the better choice, but hey, some of us don't have access to that! Case Fans: Get some of these if you want better cooling. Noctua is my favorite brand, but their fans are ugly and expensive :p
Why I don't include peripherals and the OS
Most people have a mouse, keyboard, and a pair of ear buds. Those will suffice. Gaming grade peripherals don't always mean that much, but if I were to suggest stuff, get a G710+ keyboard and a Steelseries mouse. If you want headphones, buy a cheap pair from Sennheiser, and if you want a headset, buy one from Logitech or get that super sweet Kingston Cloud II. I don't include the OS because usually you will have some way to get Windows for free, or you won't even want to use Windows. Speaking of which, 64 bit Windows is always a better choice than 32 bit Windows.