I rode it for the first time this weekend and loved it!
First time through the queue, we bailed at the last second: I needed to use the restroom, my parents were concerned about whether they could handle it or not, and my friend didn't want to leave us alone. So we just went through the games at the end and the gift shop, then left my parents at Wonders of Life while my friend and I returned. I was nervous, but decided to try it anyway. After all, I can handle the launch on RNRC -- don't enjoy it, but can handle it.
I loved the ride! Didn't feel sick, but I can tell that if I'd had a full stomach or hadn't stopped at the restroom first, I very well might have had a problem. So I advise waiting at least 2 hours after eating *or* drinking anything heavy, and if you have to use the restroom, get out of line and come back when you're done.
After our ride, we went on Journey Into Imagination, then my mom decided to try it, so we returned to Mission Space and rode it again. After this one, I was dizzy a little longer, but still not too bad. I wouldn't be able to ride it twice in a row without a few minutes' break, but that doesn't bother me.

This time, I did quickly glance around the cabin, moving just my eyes, and did just fine -- was even able to hit my mom's button on one occasion since she didn't see which button to hit, and hit the button in the empty seat next to me when that was ready. I didn't try moving my head at all. My mom loved it as well and didn't have any problems, but we both agreed my dad shouldn't risk it since he gets motion sick at the drop of a hat and especially if he gets dizzy.
I can't read in a car, can't lie down in the back seat of a car, and had been having some stomach issues the week before our trip, and was nervous about the ride. I did fine. No dramamine or wrist straps or anything.
As for the claustrophobic feeling -- the only time I felt a little claustrophobic is as the control console and window lowers down after everyone is strapped in. Once it's down, the image on the viewscreen gives a good enough illusion of space that I didn't feel confined at all.
And as for spinning -- I could tell. I don't know how, but I could tell we were spinning. Maybe it's because I know how the ride works, but there was a definite spinning sensation for me in addition to the G-forces (which do get pretty heavy, but as for "eek" feelings, I think RNRC is still much worse)
The tips I have:
*Don't ride with your stomach or bladder the slightest bit full.
*Don't look around until you know how you're going to react -- at least the first ride, stare straight ahead as instructed. And whatever you do, Don't Look Left!!! (There's a physical reason for it involving the inner ear)
*Don't lower the chest brace/restraint all the way to your chest/stomach if you can keep from it -- you'll be better off if you leave at least a finger's width between the brace and your chest/stomach, or better yet an inch.
*Breathe! Take a few deep breaths to relax as the ride starts up, and after that just breathe normally
*Relax into the seat. This was one of the smoothest rides I've been on, but make sure you're comfortable in the seat when they tilt you back for takeoff because you won't be able to move again until the ride is nearly over!
*If you can handle the launch on Rock N Roller Coaster, the loops on Rock N Roller, the spinning on the Teacups, and the video of either the DisneyQuest VR games or Star Tours, you should be fine on this ride. If you can't, then maybe. I will say the closest sensation I can compare it to was a more intense plane liftoff and banking.