Voice classes are usually divided into 30-, 45- and 60-minute sessions. Normally, students benefit from more than one 60-minute class each week to work in-depth on their voice and watch a song at the same time. This gives the teacher, and you as a student, an idea of how well you are practicing and progressing. The standard frequency of classes is one class per week.
Some people want to do more right from the start and others want to do less than that. For most people, I recommend consistent weekly classes as optimal if possible for them. In my experience, people who plan to do two or more lessons a week find that they don't actually progress much faster. It takes time for the body to develop new habits, and singing is a rather sophisticated process for the body, since many things have to align.
That said, you can speed up this process by simply practicing more. The 3-year rule for me is a singer who practices 1 hour a day at least 5 days a week. If you practice two hours a day, you can speed up this process tremendously. It all depends on how much you want it and your willingness to spend time.
Chris Glyde is a vocal coach based in Rochester, New York, who is constantly helping his students push their voices to new heights. My advice is to make sure that your vocal coach can sing the way you want or at least has the foundations in place so that they can help you do that part. The only way a good singer can stop thinking about his voice and start thinking about the songs he is singing is by training his usual vocal patterns to the point where healthy vocal technique is on autopilot. It's up to you to practice between classes and develop the stamina and vocal coordination you'll need to maintain your vocal health.