The president has the power tonominate candidates for Supreme Court and other federal judgepositions based on the Appointments Clause of the United States Constitution. This clause empowers the president to appoint certain public officials with the “advice and consent” of the U.S. Senate.
The reason that is in the president's best interest to nominate federal judges favored by most senators is that it can speed up the process of confirmation of the appointments. The President wants the quick approval of his appointments but the Senate can delay the process if the Senators have doubts and open a debate on the nominations. That is why is best for everybody to have people that have a good reputation, experience, and honorability to be nominated to be federal judges.