Good question, and total personal opinion of course.
My personal opinion: Hulk, Dragon Challenge (either), then HRRR.
I like Hulk first for two reasons: the track is below you and you get the quick launch "indoors". When I was first taking on these things, I always felt more secure somehow on a normal non-inverted track. The launch happens quick, so you are largely spared the "why am I doing this?" moment that I still occasionally ask myself going up a conventional lift-hill.
Next up would be DC. Inverted is the next step to me. Looking down 100' or more and seeing nothing but your dangling legs could be disconcerting.
Lastly HRRR. It doesn't technically go upside down like the others, but man oh man am I uncomfortable going up that vertical lift-hill. I've done it exactly once, and might do it again when I'm in the right mood. The rest of the ride is pretty conventional, but I spent most of that thinking about how uncomfortable I was going straight up. Upside down (at speed) is better, because the centripetal forces push you into the seat more. This, not so much. Did I mention I was uncomfortable?
That said, my favorite is still the Hulk. The launch is just so cool, and the thing seems to go forever. I think either DC side was over in half the time. What a blast!
Is Revenge of the Mummy an option also, or have you already done it? I would do that one before any of the others. The launch on Mummy is a milder version of the one on Hulk.