Hmm, boxing . . . every MA has its points and losses, in my opinion - even though I might as well get flamed for this - I think every style is the same at the core - but beware - to get proficient at ANY art, you will have to take it extensively for a long period - and the first art you take will be the base for everything else you will learn . . .. So if you want to really, really, learn groundwork, don't start with something like Crane Style Shaolin Kung Fu, stick with Juijitsu . . .. One word of caution - if you take an Art/Form/Style/Whatever that is 'hard',[meaning, you do a LOT of conditioning, like Muay Thai,] you WILL lose sensitivity in areas that are conditioned - [also, if you punch a lot in the art, which in your case it might, there's a good chance that you will calice over your knuckles and if you do, beware when your nose/eye itches! It hurts Dammit!] I've conditioned my foot, shin, ribs, knuckles, elbow, and chest . . . and I sometimes have regrets - that you know, we were MEANT to be sensitive in certain areas for a certain reason, and other, softer arts, like TaiChi or Judo[to an extent,] have ways of getting around that problem . . .. Anyways, good luck on your first step into the world of MA!
P.S. - Ballet DOES make you fit, and IMO, there's got to be all girls In the classes! I mean, what self-respecting male would be caught in a ballet class? Heehee! I'd join Ballet if I was you! {what would your rather do, grapple, beat up/get beaten by middle-aged men/housewives, or, dace with pretty girls that can bend waaay~ over in any direction you'd ask them to!}
P.P.S - In a serious addition, Ballet[as well as other forms of dance] and Gymnastics help out immensely in MA so you might consider taking that also.