OP, Mission: SPACE Green Team Less Intense Training seems right for you. THE simulator does shake and swing a bit, but the motion is not extreme. If something like Star Tours bothers you, there is a native 3D screen on Mission: SPACE that may bother you. If it does, I recommend looking away or closing your eyes (Note: DO NOT do this on Orange Team...keep your eyes focused on that screen during the spinning portions or you will likely exacerbate the motion sickness). Know that the Orange Team version will spin 3 times for about 15 seconds each. For the vast majority of the ride you are not spinning at all. The ride is trying to simulate high G-forces and weightlessness (you feel this a little after the high G-forces stop, but it's just the dichotomy of going from high to normal gravity). I honestly don't think you miss much doing Green Team and it is worth a try.
Both sides will have you in a very small space, so claustrophobia may be an issue. Good luck, Astronaut!