I don't like big drops, though I can certainly take small drops and even enjoy them sometimes.
I don't know about you, but for me a lot hinges on expectations. Many years ago, when I was a child, my aunt took me on a mine ride at Cedar Point and promised it wasn't scary. As soon as we were pulling out of the station, she told me, "I lied." I screamed in terror throughout the whole ride. But when I rode it again, years later, I realized it really wasn't scary at all! I think even for adults, expectations may be part of the experience.
Anyway, PotC does have the 2 drops...one of them isn't much of a drop and the other is noticeable. You might scream but the rest of the ride is peaceful and worth it. Unless you're going to physically be sick from a flume drop, I'd definitely ride once...just knowing that yes, there are drops.
The Astro Orbiter might not be comfortable for you, but if you're in the front you can control how fast the cars go up. It's usually a long line and not a big priority for most people anyway.
In DCA, Goofy's Sky School has dips/drops, like any wild mouse coaster. I'm not certain if you can tell before you're on the ride or not, but if you cannot stand drops, I wouldn't try that one. Soarin' dips like a simulator, but I've never felt at all like I'm falling. If you're deathly afraid of heights it could cause vertigo, I suppose.
If you want the ultimate starter coaster, I would try Gadget's Go-Coaster in Toontown. The entire track is visible from the wait area, so you can decide for yourself if it has a drop. It's about 1 minute from start to finish, and you're really only spending 30 seconds or so at any kind of speed. It DOES get long lines very quickly, but if you want to try coasters that's the easiest one in the parks.
Have a great trip!