Ok, looking at those things, and doing some research of my own, I dare say that iris folding would be the fastest, then Verlet (if you know derivateves and such, look at [en.Wiki][1], it becomes quite easy then) and lastly Perlin noise (I recommend simplex noise, whihc IS a bit faster).
If you want to stick with Perlin/Simplex, try looking at [this paper][2].
edit
After giving it some thoughts, I might've been wrong between on the Verlet-Perlin part, but that depends too much on the implementation and whether you calculate Verlet on a per-vertex basis. (Doesn't look like it requires that, but might be wrong there).
[1]: http://en.wikipedia.org/wiki/Verlet_integration#Velocity_Verlet
[2]: http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
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