Need some help assembling a roller blinds automation project

OK.
When choosing a DC motor for the project, does the stall current matter? All of the motors I consider getting have a stall current between 2A to 5A, and a free run current between 0.15A to 0.25A.
I have a DC adapter of 12V/1A. I could also get one with 3A if needed. Please let me know if the stall current matters and how. Basically I don't expect the motor to be stalled as it's rated power will be much more the blinds weight - The motors I consider are between 9.4kg.cm to 49kg.cm and the blinds weigh less, as you can imagine. they are bigger than average but not gigantic.
thx