I Wouldn't worry about X265 - not for 4 years or so - its at this stage still early development, and the absolute ONLY reason for it - is to get smaller size files, but the "same" quality as for example X264 - it's more aimed at broadcasting/streaming - "less bandwidth" for the same quality - but it uses a lot of cpu...
I know you mentioned no "smart tv" type things - but it's a bit of a catch 22 situation - my advice would be to replace your dvd player with what I recently bought - new high end samsung player. It is a "smart tv" - so yes, all those online services, network access etc - but even if you dont need it - it does play everything in terms of files - it's very quick - and it's a replacement of your current player, so cabling etc is a lot easier.
People will disagree - but honestly for the "non techie" - a media pc with the likes of Kodi etc is just a lot of effort that brings a lot of frustration with it. Some files work, some don't, some audio codec issues, then some video problems that aren't "quite right" - for something that "just works" - you can't go wrong with a purpose built device. Not sure what your budget is - I paid around 3K for it - there is an LG version of it (it has less features, is a year older - but about R500 cheaper)
Have a look at the SSung website:
http://www.samsung.com/za/consumer/tv-av/audio-video/blu-ray-dvd-player/BD-J7500/XA
EDIT:
Didn't mention - but this specific player still has all the analogue connections as well - just in case your tv is so old that there isn't any HDMI... or perhaps you have an older amplifier that doesn't have HDMI, but does have the 5.1 inputs..