As recommended above, focus on a good CPU. I tend to spec Xeon processors in our video surveillance workstations.
Be sure whatever GPU you get, it is not "integrated" into the CPU chip (such as Intel HD graphics), or if that is your only processor option then still get a discrete PCIe add-on graphics card.
A discrete, enterprise class (workstation) graphics card will be your best bet. I have had good results with 512MB cards (such as NVidia) and typically spec a 1GB GPU card just to be sure the system is somewhat future-proof, since they tend to stay in service in our environment for 5 years or more before being upgraded.
As for HDMI vs DP vs DVI, it depends on your application and what max resolution and screen refresh rate you will be working with.
DisplayPort offers the potential to daisy-chain monitors. It can handle up to 4K resolution at up to 60fps (though I don't know if this applies in the daisy chain application).
HDMI can handle up to 4K resolution at up to 60fps for HDMI 2.0 and above, and up to 30fps for HDMI 1.4a/b.
Dual-link DVI will, I believe, support up to 2560x1600 resolution. While DVI connections are still on a lot of off-the-shelf PCs and GPUs, that format is slowing going the way of VGA connectors in favor of the higher resolution HDMI and DisplayPort.