What was the framers' opinion on who should be selected for the highest offices of leadership?

If you go by what is actually in the Constitution, the
Framers did not have any clear opinions as to who should be selected for the highest
government offices.  They set out very few qualifications for the holding of
office.

Clearly, the framers assumed that only white men
would be elected to high office.  There are no provisions in the Constitution protecting
the voting rights of non-whites or women.

The framers
believed that only people who were in some way truly connected to their constituents
should be able to hold office.  People elected to Congress had to live in the state they
represented and had to have been American citizens for either 7 or 9 years.  The
President had to be born an American.  So clearly, the Framers did not want outsiders
running for office.

Other than that, the only thing that
you can clearly see in the Constitution is that the Framers believed that the higher
offices ought to be held only by people who were relatively mature.  This is why,
presumably, there is an age limit on each house of Congress and one for the President
(25, 30 and 35 for the House, Senate, and Presidency,
respectively).

Most of the Framers assumed that only rich
and educated men would run for the highest offices, but this was not put in the
Constitution.  They probably assumed that only Christians would run, but they explicitly
said that there could be no religious test for office holding.