Expanding a little bit on what Sleepytom is hitting on, you'll want a good MOBO to use (Oaktown has a few threads floating around with quality information and good MOBO chipsets to look for)
I recommend reading this thread:
The X99 is a good chipset.
I personally like the ASRock X99 Extreme4 MOBO.
After your MOBO, I would look into a decent processor. i7's are tried and true. The AMD Ryzen series are really starting to get a name for themselves and are giving Intel a run for their money (especially since they have a better price point than Intel's i9's)
What you said about having 8 inputs and 8 cores (one for each input).... It doesn't really work that way.
You can't tell your PC what core does what task. I believe Resolume still operates better on a single core with a higher clock speed than having a CPU with more cores at a slower clock speed (I think a lot of 3D animation software is the same, such as C4D and Vector works, depending on what style of rendering you are doing).
Joris, Daniel, or Bart, Please correct me if I'm wrong.
But get a decent processor with a high clock speed over a massive core CPU with a much lower clock speed.
*Honestly anything over 4 cores is overkill in my opinion when it comes to Live Visuals*
Getting an 18 core i9 with a clock speed of 2.6Ghz wouldn't provide you any performance boost over an Intel i7-6850k processor, which has a base clock speed of 3.6Ghz. Not to mention you would be saving a LOT of money in this part of your build.
The next step is going to be your GPU. A Nvidia GTX 1060 will handle that just fine. I prefer the 1070 for price point.
But if money is no option the GTX 1080ti would be a solid investment for the next 7-10 years in terms of power for media servers and content creation. Anything above the GTX 1080ti is just overkill and you are blowing money for no reason at that point.
My GTX 1060 laptops push well over 20 layers of 1080p@60 and still stay above 80fps in Resolume.
After the GPU, I would invest in a really nice hard drive. I always say go m.2 SSD's.
I HIGHLY recommend Samsung SSD's (the 960 Pro's for m.2 and the 850 Pro's for sata).
The Pro's have a better warranty and I believe a fraction higher speed? (could be wrong on that last part?)
If money is tight, the Evo's are still a great investment.
m.2 SSD's use PCIe lanes, but these are you MOBO chipset PCIe lanes, and not your CPU PCIe lanes. Your graphics run through your CPU PCIe lanes (sometimes this stuff gets a bit confusing)
Finally, your Ram. With Version 6, you are now available to use the full potential of your PC's memory. No longer limited to 4GB. Personally I feel 16GB is plenty of ram, but if the price difference isn't too much, Go for 32GB to future proof your build.
In Vector works, The largest show file I've built only used 12GB of ram while rendering for 4 hours (Very large festival camp ground render with multiple stages)
On version 5 I would get low memory error a few times when using memory hog FX such as Delay RGB. Now that version 6 can use more than 4GB I have yet to get a low memory error. I don't think Resolume would use more than 8GB, but I really haven't tested this. I would think my Vector works renders is more memory heavy than Resolume??
And if you have the extra money and time... Cooling. It's a small investment to keep you machine nice and happy. Especially if you come to one of my festivals out in the 112 degree heat for a week, sometimes with no cover from the sun. Quality thermal paste and proper airflow (and a good heat sink) will extend the longevity of your machine.
Your Blackmagic Decklink Quad 2 is going to use 8 PCIe (version 2) lanes
Hope some of this information will get you started down the right google searching path.
BTW, (I hate newegg as they've screwed me out of some time critical shipping deadlines) newegg has a really nice search feature on the left hand side of their website, Makes comparing and sorting PC peripherals really easy. You can fine tune your requirements then compare products for cost, makes building ht Perfect PC really easy. But I'd highly recommend using a different vendor (like Amazon) if you need the parts delivered to you by a certain week, rather than weeks later....