If you are starting with DVD-video, which I have to assume is true, since you are talking about vob files, there is virtually no advantage to up scaling the resolution of the video when converting. You will NOT be magically transforming standard definition video into the quality seen in most high definition video simply by changing the frame size.
So, if you are starting with 720 x 480 NTSC dvds, you should generally keep that resolution, as your player or tv will do the scaling for you in playback. Virtually all new equipment will obey the DAR flag (Display Aspect Ratio) and play the video correctly. Test with your specific players/tv to make sure.
What Handbrake, or Vidcoder give you in output resolution will vary a bit depending on your automatic cropping settings, and where you have the anamorphic setting. H264 and Xvid can use square pixels, which is not seen in DVD-Video, though anamorphic encoding is also possible.
So, if you want to convert to H264 in Handbrake or VidCoder, use the High Profile, set CRF to 20, change to Constant Framerate instead of Variable Framerate, and don't screw up the picture size, just leave it at Anamorphic Loose and Modulus 2 and keep the check mark in the box that says Keep Aspect Ratio.
If you would prefer to simply merge the vobs into one file, use Vob2Mpg to combine them into one file. Or use VobMerge, which will give you one big vob file, which you can then rename with an .mpg extension. Neither of these two processes will degrade video quality, since you will simply be putting the movie into a different container.
If, for some reason, you want an mkv file, and don't want to compress the movie, you can use MakeMKV to convert a DVD-Video to a single .mkv file. You will get the main movie only, and you will lose no video quality when doing this, as MakeMKV has no compression capabilities. The output file will be very similar in size to the original DVD.