for a newbee approach I would recommend handbrake.

However if you are comfortable with scripts/coding I would recommend Avisynth (windows), Vapoursynth (linux)

Some of the filters available for Vapoursynth are absolutely amazing, for Newer HD material its not usually necessary, but for older material only available in SD, the filters available can do soooooo much to improve the quality of a video. Also even some HD material can sometimes have issues and can absolutely benefit from the filters necessary to correct the problem

I love to watch music videos on my phone. I use Any Video Converter to convert into smaller file size with appropriate codec. Now I mainly use Handbrake.

DVDFab9 for converting, ripping discs. Avidemux for when DVDFab doesn't recognize files.

Format Factory for Win, recommended for everything!

I use the freeware handbrake and am very satisfied with it!

FormatFactory

any video converter is a good converter.

DVD Catalyst http://dvd-catalyst-3.findmysoft.com/

Xilisoft Video Converter Ultimate

Handbrake