Being musical is helpful. Look for a teen, teen/adult or adult beginner class dependent on your age. If you want to learn a specific style then google that style of dance class for beginners where you live. Most studios will offer hip hop classes but it is harder to find social club or street dance.
If you are just looking to free your body and build strength and flexibility for free style social dance, you could do this taking Zumba (dance/exercise) classes or martial arts like Kung Fu. Any kind of dance or movement training like this will help you get in touch with your body so you can gain strength and control over it. That will help with free style which I think us what you are talking about.
Private lessons are a serious waste of money for a beginner. They are meant for advanced students who are having difficulty in one or two things that need cleaning up in terms of technique. Then they drop it. Group classes is how you can learn best and the only way to learn to dance with others. In a beginner class everyone is a beginner so no reason to anxious. Besides everyone is too busy looking at themselves in the mirror trying to do things correctly. Nobody will be looking at you once the actual class begins. ( And you too will be too busy to notice others as you watch the teacher and work on your own dancing)