How to simply stream video from a remote server?

Use a media server rather than a standard webserver. Personally, I've played with the following:

• Vlc has a webinterface (if you enable it). By default it listens only on localhost, but changing that requires editing a single file. There's also an android app that allows you to control it. You can have it stream, it will stream subtitles, etc. Downside: pretty manual process, no 10ft interface. Upside: very flexible, best solution if you only want to use vlc clientside.
• a headless dlna system like rygel. If you install rygel and rygel-playbin, you'll be able to play your media files from any dlna-enabled device. This includes many smartphones and tablets, game consoles, and some smart tv's. Downside: no support to play on the machine itself, pretty basic. Upside: fully headless, can be configured over ssh, no gui required serverside.
• a dedicated 10ft ui like kodi (previously known as xbmc). Kodi has an official android remote app, allows you to control playback of your media files as with a regular remote, and has some support for dlna streaming too, both as client and as server. Upside: very slick interface, works really well if you hook it up to your tv, very easy to use compared to the other two. Downside: can't run headless, and the streaming options aren't as flexible as vlc.