Stock alternator up to the task? If not, how many Amps will I need?

While you can get away with it, as you said, it is not the optimal set up and can bite you. Case in point: in 2012 I was in the Mopar Muscle "Real Street" competition and one of the other contestant's cars gave up (beautiful car!), shut off and wouldn't restart after getting off the freeway. He thought it was just a bad battery, so he called back to the pits, and we had to wait, while he had a friend bring a good battery out to where we were. He got it in fired up and was good for about hour and it did it again. Turns out the alternator wasn't capable of keeping up with all the electrical goodies he had running and he didn't have a whole bunch.