Need a motor but don't know the type

[DumboJet]

What is your delta rpm both plus and minus from the 250?
If I have followed so far you want that delta rpm to occur in .06 Second (1/4 rev at 250 rpm).
What steady state rpm variation is allowed at each of the 3 speeds?
What % overshoot and undershoot is allowed during the speed change?

A very likely scenario is to be moving between [50-250-450] rpm.
I don't really care much for the precision of the speed (at any of the 3 states of velocity). An error up to 5 rpm might be acceptable (for the values mentioned previously).
I don't care much for the overshoot either (although a large overshoot than reverses the direction of the rotation might not be such a good situation to have).

These people have what you want.  There are surely much cheaper alternatives thatn them but the performance is there.  You may look at RC electric car motors.

I'll take a look. RC electric car motors might be a good idea too. I check them out too. 

EDIT : Added the " An error up to 5 rpm might be acceptable.".

[DumboJet]

T = 0.0021781709065 N*m 

It seems that for the acceleration from 250 rpm to 450 rpm it needs a larger torque (although its the same difference in rpms):
T = 1/2(0.026(0.02)^2+0)(((3*15pi)^2-(25pi)^2)/3^2)/(pi/2) =>
T = 0.0050823987818 N*m

Perhaps we should get it the other way around : from DC motors with an average motor-volume of 16 cm^3, what's the maximum torque (without sacrificing the rotation speed) that I can get and which motor provides it?

It seems I've started becoming greedy! 

[DumboJet]

Thank you all.
Perhaps a torque of 0.02 N*m or 0.01 N*m is enough and more than enough for what I want (assuming that I got the math right...).
Now it's time for me to decipher manufacturer sheets and figure out where they keep their price tags hidden... 
Someone must write a book called "Electric Motors And Manufacturer Sheets For Dummies".