Specifically answering for Nvidia GPUs:
A GTX 1070ti will have no problem at all running 3 2560x1440 monitors and 1 4K for video and desktop computing as long as you are using the correct display outputs and monitors that support HDMI 2.0, DVI-D, or Displayport.
You should theoretically be able to run 4 4K screens off of any 10XX, or 20XX series card, or a higher end 9XX series as these nvidia architectures all support 4 displays.
For the rest of the hardware:
CPU and RAM usage typically goes up as you have more applications open to fill the 4 screens, this will vary greatly depending on what those applications are though. If you update your question with specifically what applications you are using, then I can give a recommendation suited to your workload. Otherwise, any quad core CPU from the recent AMD or Intel series and at least 8GB of RAM will likely be sufficient.
One more thing that I should mention is regarding 4K video playback. It is possible that some applications or browsers could ignore the video decoding features of your GPU and work the CPU very hard to decode the 4K video. In those cases it's best to have as fast of a CPU as possible. This is likely only going to show up with outdated applications or drivers.