AP = Accessport. You don't "need" it. Its just a delivery method of getting a tune on your car. You can get a tune flashed on your car via open source tune also. Its a preference only.
Stage numbers to me are nothing but a number. That being said stages one and two are pretty widely known in the Subaru community, and typically mean the same thing. Stage 1 can be done on a stock car, usually with nothing else involved maybe other then a high flow drop in air filter. And I guess in your case (09+ WRX's and STI's) a fuel pump. Stage 2 mean addressing the cats in your exhaust. They are VERY restricting, and once you've freed up some exhaust flow with a aftermarket downpipe, a stage 2 tune can be placed on the car with very noticeable benefits.
Stage 2 has been widely proven to be a very capable daily driver modification level. Keep in mind that even a stock car can have issues with drive train, and motor. But with the right driving practices, this is a safe power level for the stock internals and transmission.