The standard way of generating spin gravity in small spacecraft concepts has been to separate the vehicle into two masses separated by a long boom or cable (booms are easier to control) and spinning both slowly around their common CG near the middle of the boom. Mass corrections can be handled by fluid pumping, moving weights, or thruster compensation.

The Discovery spacecraft in 2001: A Space Odyssey had a relatively small centrifuge that would have had to spin quite rapidly to create 1G. In the movie, there was full Earth gravity in the centrifuge, but the issues were mostly ignored. (Full credit to the movie producers for at least specifying a centrifuge at all, instead of the cinematic standard of just assuming a magical artificial gravity in spaceships.) In Arthur C. Clarke's novelization of 2001, the small centrifuge spun fast enough to generate lunar (1/6 G) gravity, a more realistic 6 RPM or so.

Dan, if your large spacecraft is cylindrical, you won't get sideways motions from axial movement on a single level. We get Coriolis force on the Earth as things move toward or away from the poles because the Earth is spherical, and every latitude has a different rotational velocity.

Moving from one level of your spacecraft to another will generate Coriolis forces, but if you're going up a ladder it won't be that noticeable. It might if you're using a fast elevator.