DVI-D can't transmit audio for built-in speakers, and is a thicker cable, and can't transmit as far as a high quality HDMI or DP. DVI-D (dual link) is also limited to 2560 x 1600 resolution, can't do 4K or above. Max res. (@ target refresh rate and chroma subsampling) HDMI or DP can do, is a matter of bandwidth, depends on the revision.
I'd sooner start the other way around, pick what monitor you want and see what it needs, or what video output you have available and pick a monitor that supports it. DP input monitors tend to cost more, but more due to their other desirable attributes than which input it has... except it could just be an older model, surpassed by a newer one with HDMI.
HDMI is the most universal, considering it comes on more video sources, new monitors, and most TVs.