Inevitably, some students fixate on a small number of clerkship opportunities, sometimes going so far as to conclude that a clerkship on any court other than the "hottest" court(s) is not worth the investment of time and money involved in applying. This has two inevitable and unfortunate outcomes: (1) sometimes these students choose to apply only for clerkships that are not well-suited to their particular interests and styles; and (2) sometimes they forego clerking entirely because they were not fortunate enough to obtain one of the handful of extremely competitive clerkships for which they did apply.
While there are unquestionably gradations in prestige between various courts, it is equally true that the vast majority of lawyers never clerked, so finding a clerkship of any stripe is impressive: lawyers recognize and value the "inside perspective" that clerks gain, whether it is in a federal or a state court. Likewise, clerking is almost always an extremely rewarding experience. Indeed, the satisfaction of a clerkship tends to be far more closely correlated with your affinity with your judge, a matter that is wholly unrelated to a judge's "prestige."
In general, the most popular cities for judicial clerkships are Los Angeles, San Francisco, New York, Boston, Chicago, and Washington D.C. That means that judges in those cities attract the largest number of extremely well-qualified applicants. Likewise, judges outside those cities attract fewer applications, and may therefore be quite willing to consider candidates with academic records that are not as objectively strong.
In general, students seem to prefer one-year clerkships; therefore, clerkships with a two-year term requirement tend to be less competitive.
Federal judges can elect to take "senior status" when, once they reach 65, their years of service and years of age, added together, amount to 80 (the "Rule of 80"). See 28 U.S.C. 371(c). The caseloads of senior judges can vary considerably: some carry a regular caseload, or close to it; others carry a drastically reduced caseload; and still others use their senior status to "sit by designation" in trial or appellate courts of other federal jurisdictions. Throw into this mix the fact that some senior judges have only one clerk, which means that even a drastically reduced caseload may nonetheless mean the same or more work for that clerk as a clerkship with an active judge. Often, senior judges will receive fewer applications than active judges, making these clerkships somewhat less competitive.
Chief judges in the federal court system (for state judges, the rules vary) are not nominated or appointed (except for the Chief Justice of the United States); instead, they assume the position for a fixed number of years based on seniority. The chief judge, at both the district and circuit level, is the judge in regular active service who is senior in commission of those judges who (1) are 64 years of age or under; (2) have served for one year or more as a judge; and (3) have not previously served as chief judge. Chief judges often have more clerks – but also a lighter caseload – than regular active judges. In addition, they have more administrative duties, which sometimes get passed on to their clerks (including speech-writing).
At the federal level, some students will reflexively apply only to judges appointed by Republican or Democratic presidents, depending on the students' own political views. Certainly if you have deeply felt ideological beliefs on which you feel unable to compromise, your clerkship year might be fairly miserable if you are unable to take direction from a judge who holds different beliefs. However, the vast majority of cases being decided do not implicate political issues. Moreover, a judge's political affiliations, or the political party of the president who nominated him/her, can be an extremely inaccurate gauge of the way he/she decides cases. Indeed, President Eisenhower nominated Justice Brennan and said it was one of the biggest mistakes of his life! Finally, many judges enjoy the experience of having their ideologies challenged, and, therefore welcome the presence in their chambers of thoughtful clerks who can ably express differing views. Consequently, in all but the most extreme cases, the best advice is to apply broadly, without particular regard to a judge's perceived politics, and reflect your own politics in your résumé (if they are important to you). A judge who is unable to enjoy alternative views will do the weeding for you!
Different judges have different management styles and philosophies regarding the clerkship experience. Personality and work habits of the judge can make a significant difference in the quality of the clerkship experience. Most judges are delightful to work for; others can be aloof, and, in a few rare instances, some can be extremely difficult. Unfortunately, it is difficult to learn about these personality traits without knowing someone who has clerked for the judge, who knows the judge on a personal basis, who has practiced before the judge, or who is intimately familiar with the judge's reputation. Therefore, if you know you want to clerk in a particular location, talk with as many former clerks or practitioners as you possibly can before you apply.