what would the initial velocity of a dropping object be?
The initial velocity of dropping objects is actually 0 m/s (or any other units you wish). Drop simply means that the object was just let go from the position of rest, at a certain height. There could be any number of examples of this situation: think of anything that one might be holding and then let go of, whether it is a set of keys, pen, ball, etc. In all these cases, the objects are termed to have been 'dropped' and have started their motion with 0 initial velocity.
If this was true, why do the objects have a certain velocity when they hit the ground? The answer is the acceleration due to gravity exerted by Earth (or any other celestial body on which one may be standing). When the Earth pulls something towards it, the object accelerates and its velocity will increase (in this case, from 0) until it reaches terminal velocity.
Hope this helps.