This thread brought up some interesting questions. I can't recommend a specific model for you, but have some knowledge:
Retail vs. Build:
Building your own rig is obviously the most cost-effective way to get what you want. That said; even with the huge number of tutorials out there, many people do not have the comfort level to try to assemble $500-1,000 worth of parts. There is also the question of warranty, form factor, “just want it to work out of box”, etc. It’s not for everyone. Do not be ashamed or feel like you’re getting too raw of a deal if you go with retail. Also, unless you're looking at small-form-factor machines, you can likely choose to upgrade components yourself at a later date.
“i7 has Hyper-Threading!!”:
So does the Pentium 4. Welcome to 2002. This essentially allows one ‘physical’ core to act as two ‘logical’ cores, (kind of) doubling the available threads. Note that ‘threads’ are like ‘trains of thought’ for your computer. Most applications don’t know how to use 32 logical cores. They know how to use 1 or 2. The big CPU factors you need to look at are a) core clock speed and b) CPU cache.
Unless you’re concerned about en/decryption, big data number crunching, or virtual machines.. hyper-threading is largely irrelevant.
i3 vs. i5 vs. i7:
Gaming: i3 does not have enough single-thread power nor cache to reliably game in 1080x. Both i5 and i7 meet the minimum requirements in available threads, speed, and cache. This makes the difference (for gaming) negligible in my opinion. There are exceptions, such as games with CPU-heavy physics, which utilize the i7 much more.
HD en/decoding: i3 is an absolute no-go. It does not have the power to even reliably stream full 1080p. i5 is adequate, but this is where you will find significant gains in using the i7. In one generation, the lowest-tier i7 will out-perform the highest-tier i5 in this respect. This is by design. If you *know* this is something you want to do, go with the i7.
RAM:
Capacity: The bare minimum should be 8GB, with 12GB if you want more HD en/decoding capability. For gaming, assuming you’re running nothing taxing in the background, 4GB will perform just fine. 8GB provides the headroom and scaling, though. This is also one of the easiest (and cheapest) things to install yourself. If you want to upgrade later, it’s easy.
Speed: There are varying flavors of DDR3 and DDR4. You will see definite benchmark differences, but they do not translate much into realized gaming performance. I can picture people reading this and facepalming. Sorry, folks. It’s true. In a custom-rig setting, this is a fine-tuning option that should be examined. In a retail-rig setting, you’re better off concerned with capacity (and other components.)
Video editing:
In the old days, video editing almost always meant you got an expensive 2D-optimized card. Now, modern applications typically utilize the same channels for 2D editing as 3D rendering. (CUDA cores.) There are exceptions, such as some Adobe products. Also, specially-optimized cards are still best for real-time 3D editing with apps such as AutoCAD.
That said; in my opinion, cards geared toward 3D gaming performance can reliably be used for video editing as well. This does not help much in the way of which card you should look for, but at least I hope this drives home the fact that your gaming setup should be fine for video editing.
Regarding the actual en/decoding of the content, you might be surprised to hear that the bottleneck is primarily the CPU. As I mentioned earlier, you’re better off with i7 if this is truly something you want to do.
Video Card (gaming):
This is probably the most difficult decision you will make, especially if you are building your own rig. There are zillions of models and variations out there, making it tough to keep track of the current “best card for the buck.” There is research necessary, including cost/benchmark comparisons..
..Or just do what I do: look for the best $250-$300 card with highest VRAM. In the lifecycle of these cards, I’ve found this to be the sweet spot. Then again, this is a hotly-debated area. You likely will not hear the same VGA recommendation from two people. In the context of a retail rig, it may help to use the VGA as your anchor point.
TL;DR:
You need at least 8GB ram and an i5 minimum. After that, performance for video editing and gaming will be chiefly dictated by the video card.
Sorry for the big post. Hope it helps.