You should be OK on Thunder Mountian, Test Track, and Kali. Only people who are extremely afraid of heights should avoid Soarin. My mom is afraid of heights, and I was concerned for her. We asked the CM before boarding if he could put us in the lowest row of seats, he did, and my mom really loved the ride!
Splash mountian is a really enjoyable ride, yes the drop is bad, but the ride is so nice. My mom loves splash, the first ride is the worst because you don't know when the drop is coming. After you get over your first ride it's smooth sailing for future rides, try riding with someone who is familar with the ride, they will be able to tell you when the drop is coming. This is the only ride I would recommend riding even though you are scared because the other stuff in the ride are so good. Most people are glad they rode Splash Mountain.
Space Mountian, Expedition Everest, Rock n' Roller Coaster, and Tower of Terror are not worth the anxiety attack! These are bonified thrill rides.
Mission Space try the tame version.
Avoid Primevil Whirl, it looks tame, but it makes a lot of people sick!