Suggestions for MKV file storage

A widely used bit of freeware called MakeMKV rips DVD and Blu-ray video into the MKV container without any recompression whatsoever - I use it because it plays better with Plex on my Roku, which is what I use as my media-to-TV solution, and couldn't be much happier with it considering I bought the Roku for $30 over two years ago and it's still going strong.

As far as remuxing MKV into more universally compatible containers (namely MP4), the solutions differ by OS, but for a simple solution on Windows you could use MkvToMp4 and on OS X either MP4Tools (which I paid for due to its usefulness) or Remux.
Note that you'll need to transcode HD audio formats into AAC for them to be fully compatible MP4s, which is the main advantage of keeping them as MKVs. Luckily all of this software can do the job without touching the video.
AVI is an ancient format at this point that primarily only supports long superseded codecs, there's no good reason to use it for anything.

 

Vidiot, MKV doesn't compress any files. It's just a container for the content. I think you may be mistaking it with MPEG-2 or H.264 which are video codecs that re-encode the video. MKV is more flexible compared to MP4 and AVI because it can store multiple video, audio and subtitle streams. But it has less overhead than M2TS or VOB files thus results in slightly smaller files. No recompression is done by MKV, only the codec (H.264, MPEG-2, etc).