I started dancing in my forties so I don't think that 14 is too late.
Because you're already a musician, you have the most important trait that a dancer needs but cannot be taught and that is timing.
You seem to be a bit apprehensive about your physical condition. Unless you have some serious underlying problem, dancing is only going to improve your health, both physical and mental. Don't let that aspect concern you.
As with any other physical skill, dancing rewards hard work and patience. However, you must always keep in mind that being a dancer is a lifestyle and not a hobby. The old canard that you'll hear is "Dancing is a marathon, not a sprint."
Do you have a potential partner?. You'll learn much faster and have more fun if you can find one. I know that most teenaged boys in America would rather shave their heads than be caught on a dance floor but a few of them will surprise you. Try to find a partner as soon as you can but don't put off starting your dance education just because you don't have one now.
Where do you live and at what kind of studio will you be studying (a local independent or a franchise like Fred Astaire or Arthur Murray)? Also, do you know what kind of dancing you'd like to learn first?
Good luck and remember that we're always here to help.
jj