Battery powering an unknown DC motor
You don't need to worry about the current input, the resistance of the motor (which can be obtained using V = IR : 12V = 1A*R => R = 12 Ohm ) will limit this. What ever 12V battery you use will only supply 1A at that resistance (V = IR again). A larger battery will last for a longer amount of time because it has more stored charge (measured in Amp Hours). Just make sure you don't use to much voltage. If you use a higher voltage than stated you WILL be allowing to much current to flow (the motor will spin faster but will burn out sooner). Which battery you want to use will depend on how long you want to use it for. For example: if you buy a 20 AH battery @ 1A it will run for 20 hours.