The correct answer to this open question is the following.
Argue a case for appointing judges and then argue a case for having them elected.
In the case of appointing judges, many experts agree on the idea that appointed is better because judges have to be neutral. They serve the Constitution, they do not serve any political party or particular interests.
Once appointed, the judges are going to ratify, so it is supposed that their integrity is double-checked.
In other cases, some arguments favor the election of judges, stating that people should be trusted to elect judges. Through this election, judges will be driven to serve the people who put their trust in them to impart justice.
If they are elected, some voices agree that judges should be elected for a determined period, so people could evaluate if they did a good during their tenure.
However, in both cases, some advantages and disadvantages have to be resolved by law experts and politicians in their respective states.