I'm going to assume you want to retain the basic human form.
You want the body to gain muscle mass at the drop of a hat, without overdeveloping it either. Muscle mass is part of what helps humans avoid energy, but you need very little effort even to lift huge weights in space - a touch is all it takes to move literally tons (2000 pounds) of mass. If they're not going to spend hours and hours of their productive day doing zero-G workouts, they need to gain muscle mass in response to extremely minor exertions. Such easy gain of muscle would be, wasteful and dangerous if food ever runs short, though.
The heart is a muscle, and that weakens in space, too, meaning that without ensuring that it gains muscle mass, heart problems that were minor, or even negligible on earth, might become critical. We don't know, but the loss of muscle mass might even be an eventual death sentence for the heart.
Next, bone density. Bones lose mass in space. Of course, you're not using them to walk on, but that doesn't reduce the potential stresses a bone might be required to support, especially in an environment where it takes very little force to move you at high speeds.
Spinal development in zero G hasn't been studied in humans because nobody think's it's worth the risk (or wants to be known as the country that risked) screwing a child up for life in the name of science. However, it's known to be related to the stresses a human grows up under. Bad posture can deform the spine over time, so it follows that no gravity can cause the spine to grow malformed. We don't know this, but you will want some controls in place to ensure that the body grows to the proper form without gravitational stresses, especially if you ever want them to walk on a planet.
There are a lot of other unknowns. Astronauts have just not spent a lot of time in space - if they do, because of the muscle loss and bone loss, they just can't walk on earth anymore. Nobody is willing to abandon a human to space forever, just for science.
However, a surprising number of animals have been bred in space, and returned to earth. Being gestated in zero G and returning to G causes serious issues - not knowing up from down, not being able to orient themselves properly, in everything from rats to jellyfish to snails. However, it seems that in rats the inner ear becomes MORE sensetive from being gestated in space, not less - it is exposed not just to downward pull, but constant unexpected yawing and rolling. Therefore, space bred rats rapidly recovered their lost ability to balance, and adapted to gravity.
I haven't found any long-term studies of animals raised from childhood to adulthood in zero-G, but I didn't look too long. Maybe you'll have better luck.
As to changes to the human form . . . I can't see a lot of people wanting to. It sounds cool, but when it comes down to it, humans find humans attractive, and nobody wants to be engineered to be unattractive. Beyond that, our brains are built to handle two arms and two legs - messing with our brains until handling tentacles is natural would go so far that I would suggest it represents a divergence of species - they would be no longer human.
Going back to our roots might be easier - feet that are better for gripping and prehensile tails might be handy in space, might not mess with the 'human' aesthetic so much, and are things that our brains already were once hardwired to handle, and might handle again easily.