So a load of 15N (plus friction), on a drum of radius 0.3m, gives a torque requirement of 4.5Nm, plus
a good margin to overcome friction, say 8Nm as a working figure for the drum. Velocity of 0.01m/s translates to
angular velocity of 0.033 rad/s.
power = torque x angular velocity = 8 x 0.033 = 0.26W
This is a tiny load, but massive gear reduction is needed (typical small motors run at 500 rad/s (5000rpm)),
perhaps 15,000:1
That also suggests worm drive (big reduction ratio in one step), driven from a 100:1 gear motor or so,
or a belt drive from a 1000:1 motor
It makes more sense to talk about the rpm of the gear motor really - lets say you can find a 30rpm motor,
which is about 3 rad/s, then a 100:1 worm reduction from that.
You can also choose a more power motor and run it slower than its full rating to get slower than rated speed
(0.26W is miniscule for a motor, using a 5W motor and running at 5 to 10% speed is more plausible).
The other drive technique that might be good for this sort of reduction is friction-drive to the rim of the drum,
using a thin spindle - that might give 100:1 or better in one step, and probably has enough friction to prevent
back-driving from the curtain weight.
A gear-reduced stepper motor is another possibility, very slow speeds are easy then as you progress step-by-step.