The actual video DVD you bought from the store (or wherever you got it) will be still playable by a regular video DVD player after you used Handbrake to convert the video to an .mp4 or .mkv file.
The resulting .mp4 or .mkv file might be not playable by regular video DVD players though, but have a look at the specifications of your regular video DVD player and if it supports .mp4 or .mkv files using the H264 codec