I have a few high quality video files in a number of formats.
I'd like to burn them so I can watch them on my DVD player.
I'd like a program similar to Nero, which can transcode the files and burn them to a DVD, as well as doing things like automatically splitting the video up into chapters.
Quality is very important: My files are 1080p blu-ray rips, and I'd like control over video and audio quality.
I think Devede would be best for you in this situation. I use it myself regularly for multiple encodes to dvd with menus.
sudo apt-get install devede
There are a few options you could try, but I have never tried to transcode blu-ray myself
Firstly there is Arista Transcoder (available from the software centre)
Kdenlive, Kino, Openshot, Avidemux, and Pitivi are all intuitive and powerful multi-track video editors, including some of the most recent video technologies.
K3b is a CD and DVD authoring application for the KDE desktop environment for Unix-like computer operating systems. (works great in Unity) It provides a graphical user interface to perform most CD/DVD burning tasks like creating an Audio CD from a set of audio files or copying a CD/DVD, as well as more advanced tasks such as burning eMoviX CD/DVDs. It can also perform direct disc-to-disc copies.
Also available from the Software centre
HandBrake is an open-source program designed to convert MPEG video (including DVD-Video) into an MPEG-4 video file in MPEG-4 Part 14 (.mp4) or Matroska (.mkv) containers.