Need an !DEA for DC Geared motor to control with Micro Controller..!

Dear buddies,
Actually iam doing a project in which a stabilized platform is needed. Ok i will eloborate it now.. We have a platform that should be stabilised with tilt sensors. Whenever these tilt sensors detects that the platform was disturbed then it should be stabilised. Here my doubt raises for this we are using some 2 Dc Geared Motors to stabilise the platform in X and Y direction.. Huh here is the question that

whats the minimum time required for the dc motor to get it started and for how much distance will the platform go up and down by how many rotations of the motors?

May be this is a basic question for you and all. Hope i can get good suggestions from you..

I have given the specifications of the motor in the attachement..

Those parameters will be determined by how the platform is designed and how the motory is loaded. The motor spec isn't worth much by itself.