If the ships are taking off from in-atmosphere they have to be rocket or winged shaped. Even if it's built in space, if it takes off or lands on a planet it has to be shaped right. There could be space stations with shuttles instead of one large ship. In the interest of money an existing space station might be converted into a generation ship or at least used in it's construction.
So, does anyone want to sit back this weekend and brainstorm a bit, as to what this ship would look like, and what all it would need? It's an incredible subject...
Shuttles would take the people to the ship, those shuttles would then stay with the space station. They'd have to be able to re-fuel and do maintenance on them. And the entire ship for that matter.
There would have to be an artificial carbon cycle and atmosphere like Earth's. Artificial gravity. Being in 0G for extended periods of time weakens your bones and changes your blood flow. I doubt someone born in no gravity, who lived there most of their life would be able to walk on a planet. Their bones, muscles and heart would be very weak.
Probably hydro or aeroponics would be used to grow some food, with some of it stored. A way to make water or large stores of it. Chemical or dry showers, water wouldn't be used for anything other than drinking and maintenance.
If they're on the ship for decades, they need building material for new things. They need technology that won't go out of date. Stuff for making habitats on new planets in case there is no wood like plants. Tools, etc. Communication with Earth would be very sparse if not end all together after a while.
If it happens it will take decades itself to build, stock and test. It would cost billions if not trillions. It's a tall order to say the least.
"Astronomy offers an aesthetic indulgence not duplicated in any other field. This is not an academic or hypothetical attraction and should require no apologies, for the beauty to be found in the skies has been universally appreciated for unrecorded centuries."