World leaders watching America make a shift under Donald Trump fall into two broad camps: those who hope that the United States will muddle through the next four years, an inexperienced president notwithstanding, and those who are eager to see Washington’s international standing and influence unravel.

The latter outcome could be averted if Mr. Trump selects an experienced and conscientious leader as his top diplomat. That would require appointing someone other than Rudy Giuliani, the former New York mayor, who is reported to be the front-runner for the job.

Before addressing why he would be a dismal and potentially disastrous choice, it’s worth reflecting on the enormous foreign policy challenges the incoming administration will face.

The Trump administration will have to create a new Syria policy, which will require deft understanding of Russia’s intentions and capabilities in the Middle East, and careful management of a complex coalition of allies fighting the Islamic State. The Trump White House will most likely be tested early by North Korea’s bellicose and nuclear-armed leader. Leaders across Europe will be watching to see whether the Trump administration is willing to let the Western military and diplomatic alliance erode, which would be a boon for Russia. Closer to home, the new White House will have to weigh the risks of turning Mr. Trump’s irresponsible blame-Mexico campaign rhetoric into policy, which would severely undermine national security by halting cooperation between the two governments on migration from Central America, law enforcement matters and counternarcotics programs.