Hi West: I don't have any advice on PAs or pickups but suggest that maybe you don't have to look any farther than a mid-60s refurbed Guild Thunder 1 or Thunder 1 RVT (this isn't spam, the one in my sig isn't for sale).
According to Jay Pilzer, the circuit topology is these amps is very well-suited to acoustic guitars; the same thing but louder so people farther away can hear but with less distortion/grunge/overdrive at higher volume settings.
I don't know enough to offer on the microphone v. pickup discussion but assuming you want an amp and, however you do it, can get a signal into an electric hose, these amps with twin 6GW8s generate on the order of 15 watts, are adequate for smallish venues, and stay distortion-free pretty well up the volume curve.
Answering the question: "How do I throw my guitar's lovely voice?" would depend, in part, on how far you want to throw it and how much flexibility you want; arguably you get less with older gear.
I don't think any of the Thunder series amps will help you much when you play Shea Stadium but all of us here on the LTG BBoard will think you're pretty cool when your amp badge matches the logo on your headstock ... we might even buy tickets ... well maybe not ...
Regards,