The easiest way to identify an AMT Enterprise is by the rough texture of the kit. This was done after the initial Star Trek: The Motion Picture version. That kit was very smooth, came with dry transfer markings, battery compartment, lights and is often referred to as the "smoothie".
The next versions had a rough texture to give a more "lifelike" surface. The lighting was removed, but portions of the hull where the batteries would go in showed signs that it was designed to be removed.
The 1701-A had a very short movie life; it was shown in the final scene (just about a minute) in Star Trek IV: the Voyage Home and in both STV and VI.
This site has some good information and stuff for sale regarding the Enterprises. Just make sure you know which kit you have; you don't want to buy a set for an entirely different scale vehicle!
starshipmodeler.biz/.../star-trek.cfm