You're sort of asking a
"how long is a piece of string" type question. Without knowing what kind of video you need to play and at what quality, it's impossible to say. You could need a full-blown desktop PC, or a chromecast might work fine.
What kinds of video do you want to play? Streaming video? Locally stored videos (Hi def?)? Blu Rays? Interlaced content?
Do you want to use Media Center on the device to take advantage of Media Center's video processing or do you just want a DLNA renderer that can "play video" (even if it's downconverted/transcoded)?
Without knowing your goals, it's hard to say what kind of device will suit your needs. An i3 or i5 haswell NUC would allow you to run MC, and has integrated graphics good enough to do basic Red October HQ for 1080 content (with some slight settings tweaks). If you don't care about running MC on the device, any number of DLNA renderers would probably work. If you want absolutely maxed out quality you'd need a computer with a high end discrete graphics card.