Personally, I would choose a professor of the class you had one of the highest scores in. Preferably one that you got positive feedback from on projects/assignments that they could possibly use as reference to jog their memory of what kind of student you are.

A persuasive letter of recommendation is going to depend more on objective criteria the professor can point to (ex. "Joe had the highest GPA in my course") rather than "Joe exhibits great leadership"

Professors have tons of students so it isn't abnormal to request a LOR despite having no personal connection. Just mention what course and when. They will probably just go back and review your grades in that course in order to determine if they have something to write about. A strong relationship obviously helps but isn't necessary.

One of the professors I chose was for a course I had two years prior. I had doubts that he would even know who I was. But I had one of the top scores in the class. I just emailed him saying who I was and when I took his course. Then I said that I felt my performance in his class would be a good indicator of my potential as a law student. He quickly agreed and it was a done deal.

Hope this helps!