Starting in 1963 all GM cars got an Alternator. Your factory original was an AC- Delco Remy model DN with the amperage stamped on the frame of the alternator. A DN sereies of alternator relies upon an external mechanical (points) voltage regulator. Over time the springs sag and the points get burnt so the unit has to be replaced.
As to your GEN light flatening the battery I doubt that. What the GEN light is telling you is that even with the ignition switched off, something is draining the battery (short, radio with a clock in it, a 1100 four chanel stero amp). Who knows?
If you know nothing about automotive electyronics take your car in to your Chevrolet Service center and hope that some one working there remembers what analog DC circuits do.