there is no difference is quality between dvi and hdmi. They are both digital. Most new monitors use hdmi or displayport.
BUT HDMI can also transmit audio and supports HDCP encryption, which is needed to play some Blu-ray content. Generally, HDMI is more convenient.
I don't really think you should be worried about the connection type. A quality monitor will come with the right connections needed to fully take advantage of the capabilities of the monitor.