One method that I've heard of is to have a committee (/"commission"/"council") select judges. The committee composition can draw from multiple branches of government (e.g. some members are existing judges and others are appointed/elected by the executive and/or legislative branches) and from civil society (e.g. appointed/elected by bar associations; in some implementations a majority of the committee is from civil society). The terms of members of the committee can be staggered.
The idea is to make it difficult for any one controversial person or party or movement to consistently dominate the committee, because in order to do so they would need to consistently dominate multiple branches of government and civil society (because the different members of the committee are selected by these different institutions) over a long period of time (because of the staggered terms).
In Texas, Justices of the Peace have no particular requirements, and are (IIRC) the equivalent of small-claims courts in the rural counties, but have had some special powers, like acting as coroner in counties without access to one. I had a government teacher with a long list of amusing anecdotes---like the JP that determined that a body with like, 27 bullet wounds had committed suicide. Judge Roy Bean was a JP; at one point someone brought in a dead cowboy who had fallen down a cliff. The body was carrying $25 and a pistol. Bean found the cowboy to be carrying a concealed weapon, confiscated the pistol, and fined the body $25.
How do you pick judges if you don't appoint them or elect them?