Start with the destination
For ordinary computer, phone or television playback, an MP4 using H.264 is often a practical first choice. Compatibility still depends on the particular device.
Consider MKV for computer playback
MKV is useful when your player supports it and you need its track or subtitle handling. It does not automatically make a recording look better.
Keep an original and a checked copy
Re-encoding can lose detail. Keep original files or discs, and check orientation, sound, subtitles and the desired time range in every important copy.