I know this is some basic stuff here, but for the life of me I can't seem to grasp the knowledge.

Basically, how do I know what type and value of a capacitor to use. I know what a cap does and how it works, just I can't grasp how to figure the value needed of any given situation.

For example.
I have a 5 volt DC motor that I need to run. Amp draw is about 60mA.
I want to be sure that 1) there is enough voltage to start the motor instantly, and 2) prevent a backlash from the coil of the motor when it stops. I know this can be done by using a cap across the +/- of the motor but I don't like just guessing at the value/type I need.

I have seen Mylar caps on these motors, i have seen Ceramic caps on these motors, and I have seen electrolyte caps on these motors, so does the type really matter?

 

Capacitors across the motor are usually there to act as snubbers for sparks from the brushes. A small mylar or ceramic cap in the range of .01 to .1 is probably enough.