I use ZoomPlayer Professional, latest version, but have been using it for years and would say any version 4 or above is fine, even 3 worked very well.
That is without a doubt the best player, no need to pay for the professional version, the free one is just as good for our needs.
For playback it is all about the codecs.
Things like VLC use their own codecs bundled into the app, which is OK, but no where near as good in terms of picture quality as you can achieve with the best codec and a great player wrapper.
The only codec you really need to pay for is the DVD decoder, although you can get free ones of those. All your codec needs can be filled from this site
http://www.doom9.org/
I personally use these codecs:
for DVD Mpeg2 video - Sonic CinePlayer 1.5
for DVD Dolby/DTS sound - CyberLink PowerDVD PRO 6
DIVX, XVID - FFDshow (latest, always keep this updated)
Also, check the easy to follow guide to setting up zoomplayer with version 4. After install it scans your PC for codecs then provides a link to their web site telling you how to configure everything in simple terms. Look out for the SVCD section, very useful.
and yes, it has millions of options, 1 of which is 'close at end of playing file', all of these are configurable by the UI.
Also check out ffdshows other features, it is not just a MP4 codec, far from it, it has hundreds of tweaking utilities in it, on a powerful machine it is great. I use a 1280x720 projector and apply 2 post process comb filters to the DVD image processed out of CinePlayer codec with amazing results.