The easiest, I believe, is a Fluxeon Annie, I had been using a friend's Bench source for a couple of years and bought a used Fluxeon Annie on this site. It is a very easy annealer to use. In the same amount of time that you load the bench source tray one case at a time you can anneal the one piece of brass with the Annie. You hold the brass in your finger, press the foot pedal to anneal it and place it in a metal pan, then do the next piece of brass the same way. Fast and simple! It takes about 30 seconds to show a friend how to use the Fluxeon Annie with the same case, it is that simple. We do a couple of hundred cases each time, sometimes 300 cases as 3 of us are using it. Every case is annealed exactly the same and every case seats with the same feel using the Annie, it was not that way with the propane type annealer. If you want automated annealing buy a Giraud Cartridge Case Annealer to go with the Annie
http://www.giraudtool.com/annealer1.htm I looked at a used Giraud on this site then figured out annealing 100 to 300 cases is just as fast with the Annie alone by hand.
I looked at the AMP, it is almost twice the price and they try to impress you with the science, not sure every lot of brass will be annealed to precisely, exactly the same hardness and if you turn your necks by 0.0005 to uniform them the anneal will change ever so slightly also as your cases grow from brass flowing they will be different. As we know brass changes as we use it. As they state it is "perfect" with virgin brass. In other words it is most likely it will anneal about the same precision as the Annie set up with the correct time as they both are time oriented. With the Amp you have a case holder to load and unload each case which will slow down the annealing process. To me that would be a pain. The Annie and the Giraud together is about the same price and will give fully automated precision. The person I bought the Annie from said the AMP did not work any better than the Annie, but they had already spent the money. Only difference was the AMP was a little faster initial setup.
The next interesting thing is building one your self or a kit, I originally built a propane annealer using an Arduino computer and stepper motor for fun. I was then going to build an induction annealer using the 1000 watt ZVS circuit board and copper tube coil ($35) with the Arduino computer board ($7) as a controller, after looking at the price of parts and time to build it, I decided I would rather spend the time shooting. Also you will have about the same amount of money in it building it yourself as buying the Annie. You will also have a very good warranty and excellent support.
All I can say is the Fluxeon Annie, I believe, has the best price performance of anything out there. It has both standard coils and water cooled coils, any case angle with the supplied ferrite concentrators, vertical case annealing with the water cooled vertical coil. It is very versatile and easy to set up. Water cooling is easy with any cheap little submersible water pump ($7), all you need is a dribble of water as it does not loose much heat. The Annie power unit is only 6 x 8 inches and 8x12 inches with the water cooled coil, small and efficient. You don't loose much bench space.
K.