Perhaps the most momentous decision the Founding Fathers made at the beginning of the Philadelphia convention was to create two separate houses in the legislature--the Senate and the House--in order to give each state fair representation.
The reason why the Framers of the Constitution wanted the selection of justices to be non-democratic is because they didn't wanted these justices to be "swayed" by public opinion, which could allow them to make judicial decisions based on what would most likely get them re-elected, as opposed to what was in the best interest of the country.