Hi Rebecca, I've never started a restaurant before, but I have started a business so I can offer some generalized input here.
I think it's important to be familiar with the industry you want to start a business within. So, gaining experience at a restaurant would be a great place to start. Because your goal is to start your own restaurant, you are in a wonderful position where gaining experience in EVERY role is important. It will be important to understand the diverse jobs at a restaurant - dishwashing, wait staff, line cook, etc. Which is to say, even if you feel like some of these jobs aren't rewarding, remember that you are doing it for the experience you gain toward your long term goal of opening your own restaurant.
I also suggest gaining some general business knowledge. Marketing, sales, financial management, etc. These skills will be just as important to the specifics of a restaurant.
I recently read Anthony Bourdain's book about the restaurant industry, Kitchen Confidential. It opened my eyes to the restaurant industry. I also found it incredibly inspiring. Perhaps that's a great place to start!