The 1" was a guess at plenty stout, possible 3/4" or 5/8" works OK too depending on the length.
Solid is stronger but a straight tube is also very good in compression. The benefit to a tube is good stiffness with less weight compared solid rod, more so at the larger diameters. 1" tube would Let the brake pedal return a little faster with less mass or momentum than 1" solid.
Use whatever size rod ends and or weld in tube bungs to suit the attachment points.
Grigg
