I have a serious height terror. I don't even do ladders or balconies. We once lived in a townhouse and I couldn't look out the rear upstairs windows, as they were 3 stories up. I had bars installed (that could be unlatched in the event of emergency) as I was so terrified of the kids even being close to them.
Somehow, DH talked me into going on Tower or Terror in 2002. I'm not over it yet. I felt like I was going to pass out for days afterward. If I think about it, I start getting dizzy.
But Soarin' is a must-do for me. I go on it quite a few times every single time we are there. I was really, really nervous prior to my first ever ride. But found it was so fun and awesome that I'm really glad I gave it a try. At no point, does it feel like you are going to fall. I could never do any real life hang gliding or anything close. This is a very safe and fun way to get the cool adrenaline rush without the fear of really falling.
I'm also one of those people that have to have something to hold on to. Just ask for an end seat, they accommodate my request for this every single time. Have a family member sit next to you so that you have bars on either side of you to use. If a stranger sits next to you, you really only get one side rail to hold. Only the movie moves, your seat doesn't move at all once the rows are raised into position. Even the highest one is not that far from the ground.
When I went on Tower of Terror, there was NOTHING to hold on to. We had seat belts, but there was no lap bar. I have heard they have since added one. I was on the end of the row, on the inside. I was freaking out looking for something to grab on to. There were metal grates to my left, but I could see the "elevator shaft" speeding by and was afraid I would cut my fingers off if I put them through the grate. This is one ride you definitely want to skip. Give Soarin' a try though.