I'd like to boost my screen space and resolution.  My primary monitor is currently a Samsung SyncMaster 2343BWX: 2048x1152 native resolution running off the DVI output of my GA-H77M-D3H motherboard.I haven't picked a monitor yet, so suppose I'd like to go up to 4k-class monitors:Will a single output type – e.g., either DisplayPort or DVI-D – be adequate for all monitors and resolution classes up to 4k?  Or would I want a card that offers both?Will any graphics card offering that output be adequate to the task?  Or do I need to look for some additional minimum specs on the graphics card?I don't do high-end gaming so refresh rates aren't an issue.  My primary purpose for upgrading would be to facilitate high-res photo editing, eventually do 4k video editing, and just get more screen real-estate.
PC support beyond 1920x1080 resolution, up to 4k
graphics cards;monitors
It should also be noted that along with GPU memory and clock speed (see Enigma's answer) that the GPU should also post what version of port the card uses.The two most popular are HDMI/DVI and Display Port. Most 4k screens only accept HDMI (no DVI) and Display port (example), research what is supported on the model you plan to buy. Most sub-4k monitors support VGA (old), DVI, HDMI and Display Port however not all at once depending on the quality of the screen.Quick reference:HDMI 1.4 supports 4k at only 30Hz (currently the most popular) (ref)HDMI 2.0 supports 4k at 60Hz (ref)Display Port 1.2 /w Multi-Stream Transport(MST) supports 4k at 60Hz (currently the most popular) (ref)Currently on the nVida side most of the 600/700 series that have a display port plug support 4k but in my experience will struggle with it if there is a lot of dynamic content.For the sake of this answer 4k is referencing 3840 by 2160, however it can mean other resolutions check here. Also use of an adapter will not grant the full potential Hz of a port see here.