That is up to you. An HD ready tv will be able to display only upto 720p resolutions vs 1080p on full HD. Standalone media players of course can play 1080p comfortably, prices range from 3.5k for the Asus Oplay Mini. Simple player USB support. No networking. Wd live I guess costs 5-6k and has LAN support too.
^ HD ready (as the 720p/1080i TVs are usually called) will not be able to show the movies in 1080p format. You will need to set your output rate to 1080i or 720p in your media player to be able to view them
LG-32LK430 should play mkv files. If it has USB movie playback feature, it is likely to play mkv. The best way to check is to go to the showroom and check.BUT LG USB movie playback won't be able to play DTS audio. In that case, you'd need a HD media player like WD Live. Or you can connect a laptop or desktop to play the movies.