There is no objectively correct way to answer this question. Selecting state judges inevitably leads to a tradeoff between two different aspects of democracy.
One aspect of democracy is popular sovereignty. This means that the will of the people is heard and the people are in charge of the government. From the point of view of this aspect of democracy, it is a good thing to elect state judges. State judges are going to be making decisions that impact the lives of the people of the state. Therefore, the people of the state should select them.
However, there is also another aspect of democracy. This is the aspect of political and personal freedom. This means that there are some things that government cannot do regardless of how much the people might want it. For example, governments should not be able to discriminate on the basis of race, regardless of whether the people of a state want discrimination. Judges are the people who are supposed to protect the people from the government. If the judges are elected, they will be more likely to give in to a majority and make decisions based on what the people want, not what the law is. The judicial branch would then be much less able to protect political and personal freedoms.
Thus, the answer to this depends on whether you think popular sovereignty is more important than political and personal freedoms.