Şehzade Mehmed, widely considered favored son of Suleiman the Magnificent, died in 1543. While it's not clear how he died, what is clear is that his father deeply mourned his death, since he built the Şehzade Mosque as a memorial to him and composed an elegy for him. This has led many to believe he was favored by Suleiman, and that he was intended to succeed him as Sultan.

What if he had?
 
Depending on when he became Sultan. If Suleiman died in 1566 regardless which means, Mehmed is 44-45 years. Not much difference with Selim. His rule may be the same like Selim with regards to foreign affairs like the conquest of Cyprus. But he may live longer, let say 15-20 years. I expect not much differences in matters of wars as OTL but the odds of being handled better than Selim II or Murad III did is likely.

Bayezid and Selim will likely try to avoid their unfortunate fate but by all acounts, they'll get strangled. Mustafa is still executed in 1553. If not, Mehmed has a serious problem. Any succession before Mustafa's death is pretty much not a lasting one for Mehmed. Thr military supported Mustafa and if Mustafa gets the sense of Mehmed succeeding (read: Mustafa and his sons death sentence) he will likely revolt and capture both his father and Mehmed and the remainder of his brothers who are near.
 
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