The length and number of sessions has little to do with your age 14 (though, if you are just starting, that is a bit late), but more on the level of play you aspire to, your attention span, the rate at which you learn and develop as a player, your ability to practice with other partners, and the amount that you can spend on lessons without having to eat Spam three times a week.
Sixty dollars per hour lesson is not outrageous, but also depends on the quality and depth of the instruction. Often times when you subscribe to a service with a long term contract (cable tv for example) you will get a special rate/discount. Not knowing this instructor's normal rate or his/her ability, I don't know if this is a good deal or just normal.
How far you will get in tennis is mainly up to you, your desire to always be inproving, you ability to soak up instruction, your perservernece in getting into shape, your genetics, height, natural athleticism and co-ordination, and so on.
Having said that, I believe that it would be impossible to reach the highest levels of tennis without a coach/instructor. So, you are on the right track.
I suggest that you continue with this arrangement for the time being and ,also, begin tournament play. Test yourself and push yourself and see how things go. You can always make adjustments in the future.
You may find that you are a tennis natural and the sky's the limit (a rare thing), or you may find that you prefer to play the oboe.
Good luck and let us us know how it goes for you.