I used to use Handbrake for all my ripping (using the file mentioned HERE to allow for the decryption). I still use Handbrake for all movies without VobSub captions (keep reading), but Freemake does a great job of directly ripping from DVD into MP4, too, and without the hassles of Handbrake settings.
Once I have Handbrake and my DVD ready to go, I need to adjust some of the settings. I use the Tools menu to adjust Options and Output File so that it dumps the finished files onto the desktop.
Then, before ripping and after choosing Source in the top left, I adjust 3 tabs.
Many times I've ripped and not had trouble with interlacing, but it's a horrible distraction when the interlacing goes awry, so now in Video Filders I just set the denoise (medium) and deinterlace (fast) each time.
Especially on a long movie, Variable Framerate can result in audio-sync problems. I haven't had audio mis-syncing with Constant Framerate yet. I set the Quality to 1500 and enjoy the results (usually my video files are between 1-2 GB).
Subtitles can be tricky. For classroom use, I can hardly imagine a situation where I don't want subtitles burned into the MP4 file, but subtitles can only be burned in by Handbrake if you click to this tab and you see "English (VobSub)"--then you can check the Burned In box and it should add captions. In that case Freemake can do the same thing and easier.
If you don't have VobSub as an option, and you only have Closed Captions, then it won't burn the titles on the Quicktime MP4 or M4V file formats. The process that I've found to work is to use Handbrake to rip to MKV format (which preserves the captions but is less universal), then convert using Freemake and making sure to check that Subtitles are On. Freemake is a step I often include anyway, to omit graphic scenes on classroom-use videos.
Finally, I have a file that I can keep on my hard drive for use in the classroom. I can also host it on Google Drive or our Moodle so that kids who miss it in class can see it from home.