For a friend, I recently researched which notebook can be recommended for Ultra HD video editing (4K UHD, 3840 × 2160 px). Here is, in short, what we found.
First priority: Intel Core i7-7xxx CPU, as fast as possible
There are three major ways to encode video: with the processor in software (Linux libx264 and libx265 libraries), with the CPU in hardware (using Intel's or AMDs dedicated features for that), or with the GPU in hardware (using Nvidia's NVENC mechanism). The hardware based mechanisms are much faster. For example, one comparison test was 55 fps on a i7-5930K CPU and up to 540 fps on a NVIDIA GeForce GTX 980 GPU [source
]. So a factor of 10 can be expected.
However, hardware encoding is somewhat limited in terms of features, so the same video quality will have a bigger file size, or for the same file size, you get less quality. For example, Nvidia NVENC supports B frames (some kind of small, compressed frame type that reduces video size by approx. 30% at the same quality) only in H.264, not in H.265 [source
]. So the enthusiast video editor will probably want to do the final encoding runs in software on the CPU, which can be 20 times slower, but gives better quality for the same file sizes. Preview versions can still be created with the CPU or GPU hardware support, but do not need as much computation power as resolutions will be lower. Also, reportedly the primary, most powerful competitors are Intel CPU hardware based encoding on Kaby Lake processors (Core i7-7xxx) and GPU Nvidia Pascal GPU based encoding on Nvidia GeForce GTX 10xx graphics chips, and the best of both are approximately equally powerful. There seems to be better software support for the Nvidia solution though (but that is just a rough impression).
As a consequence, when you want the best quality and accept a long final coding run in exchange, the graphics board does not really matter much, it "only" has to be suitable for playing back 4k video and perhaps applying some live effects on them. So even a "previous generation" (Maxwell based) Nvidia GTX 960 will do, as some models have in this list
of 4k editing notebooks. You will however want the best and fastest CPU you can get, which (in gamer notebooks) seems to be approx. the Intel Core i7-7600HQ (2.8 GHz).
Second priority: display
The next question is what display to get. Choices are between 15" and 17" displays, and for both between Full HD (1920×1080) and 4k Ultra HD (3840×2160) resolutions. Without a 4k display, you obviously can't watch your 4k video in full glory while editing, but even with a 17" 4k display, pixels are so small that there is very little to no optical difference between a Full HD and a 4k Ultra HD display (as reported by gamers). You will have to zoom into frames to see quality differences anyway. But the price difference is sometimes just 200 EUR, which might make the 4k Ultra HD display worth having.
Third priority: main memory, mass storage
These things can be upgraded as needed, so you don't do a final decision on purchase. 16 GB DDR4 RAM and a "128 GB SSD plus 1 TB hard disk" combination seem a reasonable minimum though. To speed things up, the SSD should be sufficient for the operating system, software, and the video files of your current project, while the (cheaper and larger) hard disk would hold all the archived video editing projects.
The most interesting models (high performance but at the lower end of the possible price range) that we found are these: