It's not only calcium deficiency - muscle atrophy is another serious problem that also results from the lack of gravity.
If you haven't already, give the book Ender's Game a read. I found it pretty interesting, though not at the time that I first read it, since I was around jr. high age. I read it a second time in high school, IIRC. The way they deal with space travel is pretty interesting.
Centripetal force is definitely a viable option. Remember that you need some kind of force that pushes you against a surface, and centripetal force would be the easiest, most familiar way to achieve that. To achieve desirable results, though, a sufficiently large system would have to be spinning rather fast, since centripetal force drops exponentially w.r.t. radius.
The problem with a greenhouse is that it requires sunlight. This would be a more prevalent problem if you plan to travel far from the sun. Yes, you could use artificial lighting, but for that you'd need to produce energy. The most efficient form of self-sustained energy production would be nuclear fusion, which would be like having an artificial sun, but of course that is currently not feasible. Nuclear fission would make more sense in a spacecraft, but just how long would that last you?
Right now I'm envisioning a large, donut-shaped structure of about 1km in diameter, with a hole in the middle of about 500m in diameter, and some kind of durable transparent material lining the portion of the structure that faces the inside. In the middle, outside of the structure but inside the hole, is where the artificial sun would be. The structure would have several floors, of course. Assuming we can build such a structure, here are some things to think about.
I'm not sure how many people that would sustain, but for long-term travel, the initial inhabitants should consist of young couples and fill about a quarter to a third of the structure, assuming the structure is capable of providing resources to everyone when the structure is full. This way, several generations can live on the ship, with the younger ones taking over the task of maintaining the structure as the older generations pass on.
Food would be an interesting problem, as just eating fruits and vegetables grown in a greenhouse can't exactly be good for your health. You need some kind of meat and dairy products, or everyone will die upon setting foot on some unknown planet because of the lack of energy. That means you'd have to bring some livestock onboard, enough to feed everyone, and enough to breed.
Water is the next big thing. Think about everything you do that requires water, other than consumption - cooking, washing, and bathing are the main three. You'd need to be able to cover that for everyone onboard, so there needs to be some high-scale filtration system.
Waste is another problem. How much garbage do you throw out every day? Where's all that going to go? You can't just burn everything. Chuck it into the artificial sun, perhaps? And what happens when stuff breaks down? Nothing lasts forever. You'd need multiple tradespeople on board if you intend to keep everything running for a long time.
It would not make sense to shut off a nuclear fusion reaction for 8 hours every 24 hours because it takes so much energy to get it going, so either it's constant daylight or sleeping quarters would have to be at the far end of the structure, away from the sun. That brings up another problem - travel. Perhaps you can have several 500m long elevators that run from top to bottom. They would have to be incredibly energy efficient to avoid putting a huge load on the energy source.
Finally, recreation. This is not as trivial as you might think. Do you honestly expect people to be content with a lifestyle without any kind of entertainment? No sports, no TV, no Internet, no video games... perhaps you'll have books to read, at least.
In the end, you're practically creating a miniature planet, just in a different shape. Makes you realize just how much everyone depends on everyone else, huh? Maybe it'd even be easier to just propel the Earth - that way you'd only really need to think of a viable energy source that you can reproduce all over the planet.
Edit: Just gave it a read. The 1G acceleration idea is rather interesting, but rather dangerous.
For one, at ~10m/s2 acceleration, you would reach the speed of light (300 km/s~300 000km/s to three significant digits) in ~30 000 000 seconds, or about a year, assuming you can sustain that acceleration. That means you can't accelerate at 1G and then turn around just once at halfway - you'd have to do this repeatedly. That means that if you are heading somewhere outside of our galaxy...
And for two, navigation in space is more difficult than the guy makes it seem. There's very little friction and air resistance in space - people can't seem to grasp that fact. At those speeds, if you're heading straight at an asteroid, you're sure to die. You can't suddenly dodge it, even if you were going at a regular walking pace, unless you have some incredibly specialized thrusters pointing in all directions.
And finally, for three, it's very rare that you'd be able to travel in a straight line all the way to the destination. Take that into account along with the first point, and you end up with some very complex calculations to determine the optimum path.
