Simple, easy to configure streaming server for linux - just transcode & stream
https://www.digitalocean.com/community/articles/how-to-stream-videos-with-nginx-and-jwplayer-on-centos-6 makes Nginx look pretty simple to set-up as the streaming server. I've not used it but I have used jwplayer and that worked well for me (I was streaming from vlc/vlm). Another good option for the player end would be jplayer.

Web Videos via Watch Folders Transcode is a reasonable approach to the transcode issue.