BEST Video Resolution + Format For Small File Size? [.mkv to .mp4]?

[slow_mo_panda]

I have the Samsung Note 2 which has a screen size of 1280x720 and I have several video files in 1080p and some in 720p mostly .mkv files, and I am looking to convert them to the smallest file size/format possible while maintaining a quality of image that does not take away very much from the 1080p sharpness. Does anyone know how to do this? I am using the freeware program 'Any Video Converter' which allows me to convert to almost any file format, usually I use .mp4, and I can set the resolution to anything, the video codec can be set (mpeg4, x264, or xvid), and Video frame rate, and Video and Audio bit rate, etc.
Any video pros out there who can tell me what to put the settings at and maintain at least the 720p sharp image?

Thanks a ton!

 

[YouGonaEatThat]

Try Handbrake. I use that to convert to mp4 regularly. I'm not totally sure about getting the resolution you want though. I never really got into the settings and all that.

HandBrake