Well your first post will be my first post as well. I did it the same way you are envisioning ( almost). I found a club with a 172 that would allow a student pilot. It was a great plane to learn in and satisfied my flying needs for the first two years /150 hrs. I then began looking for greener pastures and wanted to go faster. I never really thought much of the mooney and I heard they were expensive. Then I stumbled upon a 1962 M20c. I fell in love with the manual gear and simple flaps. I had no experience with adjustable props but it's not too hard to figure out after 3-4 hours of flying. As a low time pilot with no retractable time, AVEMCO insurance charges me $1700 a year. I have found other quotes closer to $1200 and I will be switching to one of them after the this quarter. Fuel burn is 2-3 GPH more than 172 so that is a consideration as well. Over 50 hrs that is 150 more gallons you will buy to get your license.
As for your first plane, I think you will be much better served with a trainer type. A 150,172, or piper 140, etc, will be more then enough when you first start. If, after your first 20 hrs, you still think you need a mooney right now then get one. I loved the simplicity of the 172 and it was just easy to fly and confidence building. I know for certain the mooney would have made me consider quitting on the early "hard" days of pilot training.
Let us know what you end up doing. Good luck!