VLC can be setup to do this...
Go to preferences, in the first tab "Interface", in the look and feel section there's an option to show the control bar in fullscreen. (it shows for a few seconds and then auto-hides). It could be beneficial to leave it showing, but if you don't want anything on the screen you can uncheck the box and rely on hotkeys for control. (or programmable remote, if you have one available)
On the same tab, scroll down to the playlist settings and check the box that says 'Pause on the last frame of the video'
Now, if you left the control bar showing in fullscreen, to start the next video you could use the mouse to click the 'next' button. If you chose to turn the control bar off, then you'll have to use a hotkey to start the next video... the default key is the 'n' key. (Cannot be set to a mouse click)
Some other options you might want to check... go to the "Video" tab. Here in the 'Display' settings you can check the "Fullscreen" box, this will make VLC automatically start playing the playlist in fullscreen mode.
Click the "Subtitels and OSD" (on screen display) tab... at the top are 2 boxes. The second box controls if you want the title of the video to display for a few seconds on the screen when it starts. If you don't want it to display, make sure this box is unchecked.
The first box "Enable Onscreen Display", if you uncheck this box, you won't see any information displayed on the screen during playback, not even the play or pause symbols.
NOTE: Sometimes changes might not take effect immediately. If you change a setting (like turning off the control bar in fullscreen) and then click apply, it may still show until you close the player and open it up again.