Yes, it does depend on the client’s goals, finances, and self motivational levels. However, 2x per week is a great base to clients to see results (if they are doing the rest of the work on their own) (or even 3, but that may not be feasible for many people). You will find that as you train, you will run into all kinds of clients and their needs are all different.
I respectfully disagree with Steven about training times being limited by 5-7. You will see clients wanting to work out at all different times of the day. I train starting at 5:30 a.m. through mid-day (do not work evenings), and my schedule is booked every day. You may have people that train before work, people who’s schedules are flexible (work from home), stay-at-home moms, retired individuals, and those who work out on their lunch break. Then you also have the evenings for those clients after work. So, be prepared for the hours you are available, and go from there.
Budgeting your time for clients, and actually filling your schedule with them are two different things. It may take you some time to build a client base.
Best wishes to you as you start your fitness career!