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.