To give a complete answer, it will be helpful to know what boat you want to put the pump into, is there a pump already in it, engine information meaning Hp at what Rpm and what you want do with the boat.
There are members who know much more than I but the short answer is the JG is later design pump that can handle more power than the JC and will allow easier modifications like diverters, and snoots. If your engine makes less than about 500 Hp, the Hp capacity of the pump is not an issue as either one will be reliable.
"A" impellor compared to "AA", the "AA" will move more water at lower Rpm than the "A" and will require more torque at lower engine speeds. So you are back to needing to know more about your engine.
Used Vs rebuilt Vs new. Depends on how deep your pockets are and how mechanical you are.
Sorry for not being able to provide complete answers but it is a start. IF you are able to provide more information there will be plenty of help from the forum.
As I understand it the only difference between the JC and the JG is that the JG has a split bowl, a desired feature for those looking to put a droop snoot on. In regards to the difference between an A impeller and a AA is that the AA, providing you have the power to do it, will turn the same speed as an A but at a lower rpm, think of it like the rear gears of a truck. The goal is to have the correct impeller that corresponds with the hp and power band of your engine. I just put an A in the pump that came with my boat and took out the worn AA as I didn't have the power to turn it so it really was pig out of the hole. In regards to rebuilding vs. a new one, I find that for most applications the rebuild is way more bang for the buck and will perform the same at half the money, a pure racing application might be different.