As a classically trained ballet dancer for 19 years, I must disagree with a lot of what has been said about ballet training being detrimental to standard dancing. Yes, there are some things that a ballet dancer has to "unlearn" for standard (ie not to turn out, not to pull the knees taught in rise), but overall, the basic concepts that you will learn from ballet are very valuable to standard dancing. I actually teach a ballet for ballroom dancers class that focuses on the aspects of ballet that help in both standard and latin.
The posture in standard for the lady is very similar to a position that's used as a stretch called cambre in ballet. The arms are held through the back in both dances, so I'd say from the shoulder to the elbow for both man and lady, the arms are the same for ballet and ballroom. In fact, taking ballet would build up those muscles you need to hold your arms since you have no partner to just let them drop on.
Ballet is not all about being lofted. There is a center of levitation (ribcage up), and a center of gravity (around the pelvis area down). Ballet dancers are taught to use the floor, as you need to do in standard. Also, you develop a strong core in ballet and learn how to hold the hips up so the legs are free to move (what's needed in standard to achieve movement).
In regard to being between the feet, in ballet, you never allow the tailbone to cross the center line, which is similar in all dance since it throws you off balance. In very fast movements, ballet dancers keep their weight centered between the feet so that it's easier to move quickly, so once again, there are similar aspects to ballet and ballroom.
Above all else, learning ANY dance style alternative to one's primary style only helps strengthen the primary dance style. In learning a new way to move your body, you start to understand how to use your muscles more and can start to connect things you've learned in the primary style. Not to mention that learning to dance to different music helps with the musicality. So I would say definitely take ballet.