a media player is a device that plays the media to the tv. just like a bluray player, that reads from the bluray disc and sends that signal to the tv... a media player does the same thing but can get the video from a few different places instead of a bluray disc. a media player can get its media from the internet, internal hdd, usb hdd, or over the local network (cable or wifi) from a pc or nas. roku, amazon fire tv, apple tv, wdtv, on and on, are media players.
you can look on amazon for media servers, those will bring up nas devices. the alternative is to install software on a computer to do the same thing. the media server is like a file server, it stores and streams the media over a network to the media player. if you aren't interested in that, then you need to look for a media player with an internal hdd, and/or one that accepts usb hdds. i think the sony FMP-X10 works with usb hdds.
there are some 4k media players on amazon, but i dont recognize the brand/company, so i probably wouldn't buy any. most on there are like the roku type, they want network or usb hdd. they have no internal hdd. if the sony or any other you are looking at, is too expensive, you can wait and there should be more 4k players out to drive down prices.