BTMR is definitely the next step up from Barnstormer, so that's a good place to start. Then if you like that, you can move on to other things.
Splash Mt might be a good choice. It's a pretty tame ride. the big drop you can see is the worst part and just when you start to not like the feeling you get from the drop...it's over. There are a few small drops in it as well. It's my favorite ride.
Test Track would be ok as long as you like fast. It's smooth, you can see where you're going, there are no dips....but it does get up to around 65mph. If you'd enjoy riding in a convertible on the interstate, then you'll probably like Test Track.
AVOID Primeval Whirl at AK. It's SUPER jerky. It's tame...but I found it to be extremely uncomfortable because of the sudden turns and stops. My neck hurt when I got off it.
I wouldn't recommend EE or Space yet if you're wanting something tame-ish.