Who shall I ask is an important question. Choose faculty members or administrator supervisors who know something about your ability to write, read, research, analyze problems, argue, and speak in front of groups. Perfunctory letters from "famous" people won't help.
Confidential letters are probably (slightly) better than non-confidential letters. But make sure your potential "recommenders" are able to write a strong letter on your behalf.
Don't assume the faculty member or supervisor knows everything about you. Provide them with information which will help them write a good letter. Make a list. Show them the paper you wrote with the great teacher comments. Remind them about the courses you took. Have a conversation about your plans. Is there anything distinctive about your course work, your experiences, your extracurricular activities, and your interest in law school? Specific details count. It’s what distinguishes you from all of the other candidates with similar GPAs and LSAT scores. Do as much as you can for the person who is recommending you. You want your letter to stand out.
Most important: ask for the recommendation well in advance of the deadline. The people you ask will be busy. Check on progress regularly. Some of the people you may ask will be busy and forgetful. Remember, in the last analysis, it's your responsibility to see that a good letter of recommendation arrives on time.
You will likely be applying to at least six schools. Make sure that you've filled out and organized your packet of forms.
If you think it's appropriate, make a copy of the following and give it to the people who are writing your letters of recommendation.
Writing a helpful letter of recommendation for law school
Virtually all law schools divide their candidates into three groups: clear admits, possible admits, and clear rejects based on LSAT score and GPA (with LSAT score being the more important factor). Your letter can make the difference between acceptance and rejection for candidates in the possible admit category.
Law schools will already have candidates categorized by LSAT and GPA when they read your letter. You can make a good guess about what that categorization is by looking at the Boston University Law School Locator.
Candidates will be helped if letters contain specific, comparative information. Quotes such as "One of the four or five best papers in the last two hundred I've looked at" or "Much more intellectually curious than any student within the last five years," etc.
Candidates will be helped if one can point to something distinctive in their course work, or experiences, or interest in law school: anything that might make them stand out from all of the other candidates with roughly the same GPA and LSAT score.
In some cases, candidates will be helped if one can make a plausible case that their GPA or LSAT score doesn't reflect their true ability: the candidate took much more demanding courses than average; the candidate had a serious medical problem in her sophomore year, etc.
Finally, if as a recommender you know that one of the schools is the candidate's first choice, you should include that information in the letter to that school.