Handbrake's good for converting to MPEG and AVI formats, with the exception of MPEG2 (DVD). It's not a suitable program for copying DVDs -- but is totally suitable if you want to rip a DVD into some format you can watch on your computer.
I use both MTR and FFmpegX. I find it best policy to rip to an image file, then burn from the file. If you do burn a coaster then, at least, you don't have to rip the disc again.
he has a video explaining which programs to use/get and what to do to rip the dvd to your computer and reburn it to be playable in any dvd player.
you'll need
MacTheRipper to rip the dvd to your harddrive
dvd2oneX to make an image out of the rip (and size it down to 4.4gb if it is a DL DVD rip)
any burning utility (disk utility will work fine) to burn the .img onto a dvd