It was under Suleyman the Magnificent that the Ottomans conquered Hungary and even threatened Vienna. This was the high water mark for the Empire in terms of territorial conquests. He also conquered what is modern day Iraq, and the period of his rule, which was most of the first half of the 16th century, is often seen as a cultural high point as well.
Sultan Suleiman the Magnificent and Sultan Mehmet the Conqueror.
I vote for Sultan Ahmed III
The Ottoman writers guild denounced the printing press as "the Devil's Invention." Their objection caused a 53-year lag between its invention by Gutenberg in Europe in the 1440's and its introduction to the Ottoman society with the first Gutenberg press in Constantinople that was established by the Sephardic Jews, who had escaped from the Spanish Inquisition of 1492. However, Muslims did not use the printing press in the Ottoman Empire until the 18th century. In 1726, Ibrahim Muteferrika convinced the the clergy on the efficiency of the printing press, and later submitted a request to Sultan Ahmed III, who granted Muteferrika the permission to publish non-religious books despite opposition from some calligraphers and religious leaders. Muteferrika's press published its first book in 1729, and, by 1743, issued 17 works in 23 volumes (each having between 500 and 1,000 copies.)