"As much current as possible" and "as small as possible" are
not compatible goals. A local optimum is the best you can
hope for, and that needs clearer goals.
A scrounged DC motor (like from a cordless drill) might be
a good approach, and the higher the battery voltage the
higher the motor-as-generator output. Without a gear (or
belt, or ...) reduction you will be hard pressed to get useful
voltage out of a small slow turbine. And a small radius turbine
would probably not have enough breakaway torque to spin
the drill head with its nice integrated gearbox, alas.
You might need to add a boost converter at the motor
output (low voltage capable) if you can't count on wind
speed and turbine details to get you the RPM to make 5V
(assume the phone is USB charged). You might also need
a 5V shunt regulator as a backstop in the event that you
do find "good wind".
I'd say to start with the turbine you can tolerate (size)
and put it onto any motor you can find, and measure the
open circuit voltage and short circuit current you can get.
This would be a sanity reading, to drive "next motor"
selection. You might also like an intermediate data point
like current@5V (the end game) to compare to the phone's
real charging draw, and some idea of what the phone's
response to undervoltage and overvoltage might be -
nondestructively obtained, you hope.