You can create a very nice simple solution using radio control servos. They come in many sizes, but even the small ones have enough torque to move a big arm to move a cd.
The real bonus with servos is that they normally have 180 degrees of rotation and internally have a variable resistor (rheostat) for positioning feedback. Positioning accuracy is normally within 1 degree of rotation which should be fine for a cd loader.
For picking up the CDs, nothing will beat a vacuum. I recommend a small battery powered vacuum cleaner. Funnel the suction into a 1/4 inch pipe. At the other end of the pipe a one inch diameter cup should provide more than enough lift from the small amount of suction.
As for the pile of blank CDs to be burnt, I would advise in moving the pile up rather than an arm down to it. probably having the top blank cd about 1/4 inch higher than the cd tray - By doing this, the arm only needs to rotate in one axis and the vacuum should be enough to suck the cd back out of the tray.
Now, for the electronics. For the servo control I suggest an rs232 serial servo controller. I've used the one from http://www.basicx.com/Products/servo/servo8t.htm as it also gives back torque information from the current draw.
For the low sample rate digital i/o, i suggest (for windows) inpout32.dll which is a dll to give you direct access to the bits of a parallel port. This will allow you to turn on the vacuum at the correct time and possibly sense when cd's have run out. Note that a parallel port can sink more current than it sources so for outputs you should connect to the 5v power line and set the output pin to 0 to turn on the output and 1 to turn it off.
The other nice option, which is very, very simple to interface and very cheap is to get hold of a picaxe from http://www.rev-ed.co.uk/picaxe/. These use a very simple programming language (a BASIC spin off) allowing you to read serial data in and control the servos and digital I/O on one chip. Last time I used one, the language was a bit simple - if statements had to jumped labels, else didn't exist.
If you do use a microcontroller and servos, it is best to use a dual voltage power supply as servos are noisy and can cause the microcontrollers to reset.
As for switching loads such as the vacuum on, you'll need to use a mosfet or (if money is no object) the simpler option, a solid state relay.
All digital inputs you use on the microcontroller should be pulled either to +V or ground with say a 5k resistor so they never float.
I cannot stress how simple and cheap the picaxes are. They have a built in interpreter so although code space is minimal on the small 8 pin units, they are programmable via a simple serial lead.
Good luck. Once you get into automation control, you'll never be able to stop. I'm in the middle of building a 3 axis CNC router so I can cut parts for other projects (I tell my girlfriend it's so she can cut out xmas decorations!).