I recently used my Canon XF305 to shoot a large number of landscape videos and now want to prepare them in FCP for a 60" Sharp Aquos LCD.
...I am wondering how to optimize my files for this display. How large can the files be? I'd like to have the least amount of compression possible.
Your LCD monitor is 1920x1080 at rec709. The images you shot on the xf305 are the same specs. No amount of transcoding or rendering will give you more detail. In an ideal scenario, you must show the videos as is.
For a one-render situation (assuming no effects have been added), an authored blu-ray disc might be acceptable. A lot of people won't be able to tell the difference. To test, I suggest you go this route (with standard render settings) and only if you are unhappy with the result should you try this:
If you are going to edit on FCP (which transcodes everything during ingestion into its unnecessary mov wrapper), the best you can do is render your timeline to an avi wrapper (which can also be read by modern DVD and Blu-ray players), in the MPEG-2 codec, with the same bit rate as your source footage, in the same frame rate. This file can be copied to a Blu-ray so that it behaves like a data disc instead of an authored blu-ray disc. If the file size is smaller than 8GB, you can even get it onto a DVD as a data disc.
HDMI is not a robust connector, and is prone to many issues. This must be your last option.