MKV by itself should not be a problem (it is like AVI), the video format being decoded is what will. Anime and MKV however often means H264 video which taxes most systems.
A few things:
H264 has post processing in the spec, make sure the additional stuff (which I suggest for xvid) is not on or slowdowns will occur. Likewise you can often disable additional processing if you really want (not suggested by me).
Chances are you have FFDshow installed (most packs and definitely CCCP) which will have it on.
You already were recommended coreavc and it is good. Be careful if getting it by less than legit means as I have seen a lot of malware spread by such a thing.
You mention text/subtitles, anime is tricky and many groups use stuff like ASS (advanced substation alpha) as opposed to the bog standard SRT and vobsub (idx and sub files) which everything plays.
I suggest CCCP here rather than tangling with a manual setup as the people doing it know what goes but make sure to uncheck the H264 stuff when installing it again or you will have just rendered your coreavc install pointless. If you do double click on the FF icon with black text that appears in your system tray (the video one) and disable it from there.
Also some installs can check pre buffering, it is not usually necessary so double click the green arrow in the system tray and under the misc tab is the option to disable it.
Also something like geexbox, XBMC and the like (linux media distributions) will also do well and in most cases you can run them from a livecd.