I have periodic problems with vertigo (especially from spinning motions); here was how I fared when we were at WDW in September.
I avoided the tea cups like the plague since similar rides at the county fairs have been making me ill for the last few years. I did ride Astro Orbiter and would not recommend it. I was definitely feeling the effects when we got off.

I had forgotten how fast it went. I avoided Body Wars, but couldn't resist going on Star Tours. To my suprise, I was fine on Star Tours (closed my eyes in a couple of parts), so now I wish I had tried Body Wars.
We did not go on Space Mtn, Mission Space, Rock N Roll Roller Coaster because DD was too short, but I think I would have been fine on all but Mission Space. Usually roller coasters aren't too hard on me.
I rode, and was fine on, Goofy's Barnstormer, Buzz Lightyear, Dumbo, Triceratops Spin, the carousel, etc. On Aladdin's carpets, we got to going a little faster than we had on Dumbo and that did bother me a little.
So, overall, I didn't have many problems. I would just say to definitely avoid Astro Orbiter and the tea cups, of course. Have a great trip!!