If the videos can be played in
omxplayer, you won't need to start an X session. Just type
omxplayer -hdmi http://video.example.com/video.mp4 (substituting whatever video URL you want) and it should play. This does require you to know the video's "final" URL, not just the URL of some page that embeds it, but the huge advantage of
omxplayer is that it uses the Pi's GPU rather than its CPU, hence it can play high-definition videos even on a Pi Zero (or Zero W) as long as you've set
gpu_mem high enough in
config.txt (384 works well, although on a Zero that means you'll have only 128M left and had better not try to run an X desktop without a swapfile). On the 3, CPU and RAM is not quite so much of a worry as on the Zero, but even so I expect
omxplayer will work better than VLC et al for a good few videos.
For the final tweak, find out the native resolution of your projector, find out which HDMI mode number is closest to that resolution, and use the
tvservice command to select it. E.g.
tvservice --explicit='CEA 3 HDMI' gives 720x480 (16:9) which works well with the Miroir Mini Projector. Run this before running
omxplayer and you should get some nice clear video renditions.