Use 624x352 for HD & wide
544 x 400 for SD
Check Deinterlace
Sound 44100, 128
bitrate 1000 for HD
bitrate 800 for SD
FFmpeg 29.97 not same as source cause it ain't
Search my posts for my Handbrake tutorial.
I suggest that there is no one grouping of settings that work best when ripping a DVD.
I would only force the 29.97 fps framerate if I /know/ the DVD was authored expecting to display at 29.97 (most animated material, ironically). Most feature films should remain 'same as source', as it is supposed to be 23.94 fps, and making it 29.97 can introduce some artifacts. TV shows, I would do a sample encode of maybe 5 minutes before deciding, as some are authored to display right when using 'same as source', and some aren't.
Be careful of the deinterlace flag, as Handbrake has a pretty poor deinterlacer when used on animated material (but unfortunately, animated material needs the deinterlacer the most).
And Multimedia, as the OP posted that he/she is trying to get as close to DVD as possible, can we try to avoid the anemic bitrates? In my experience 1400Kbps H.264 works best for SD/DVD material, and keeps a small file size. If you use the x264 (iPod) setting, these files will work with your iPod as well (using MediaFork). If you aren't worried about iPod compatibility, I would use 1700Kbps H.264, and let Handbrake use the largest frame size it can.
As for why you are seing what you are seeing, Handbrake is programmed to use a maximum of 720 pixels wide /or/ 480 pixels high. So 4:3 content becomes 640x480, while widescreen content winds up being 720xSomething. DVDs are authored 720x480 in what is called 'anamorphic' encoding. The DVD is forced into one resolution, and then a flag set saying 'I am this aspect ratio'. The DVD player will decode using that aspect ratio. The advantage is that NTSC DVDs will always have 480 pixels of height, and the width will get stretched as needed. The human eye is supposed to see height detail more than width detail, so the stretching done is supposed to be unnoticable.