So I've decided that I want to build the lever style of press that was posted in the video earlier as I have found pictures of them from as early as 12th century.
I reckon that the member that is going to have the most force on it is going to be the lever itself. Everything would then be sized around that.
Here is a simplified version:
http://i1222.photobucket.com/albums/dd481/Weaverofduart/pressbeam.jpgI'm not concerned about deflection but I obviously don't want it to break so everything else is important. Unfortunately I'm at a bit of a loss to calculate everything except deflection.