Hi gespit,
Before I got into 3D, I was a robotics engineer, so one of the first things I tried animating in Maya was an industrial robot. My earlier experience was mainly with ABB and Motoman robots, but I'm assuming that Kuka & Fanuc machines are pretty much the same.
I like Joojaa's suggestions - I did it roughly similarly. Because a standard 6 axis robot has only one degree of rotational freedom and no translation freedom at each joint, I first locked off all the other degrees of freedom on my model. This meant it could only move the way a real robot would, but did cause the IK solver a few issues.
Because there are multiple ways of controlling a real robot I tried to emulate these in Maya. The easiest was of course joint by joint FK control - I created set driven keys for each joint so that I could make it move only as far as the real robot joint would go. The next two are different versions of IK - one in world space and one in the coordinate system of the manipulator. These are a bit more difficult and more like what you've described. To do this I set up a single IK chain between the shoulder and the wrist of the robot (RPSolver) and used the equivalent of a no flip knee to get the rotation at joint 1. the downside with this is that if you look at a real robot, depending on the make and model, the joints are not necessarily in a single plane.
The other difference between a real robot and a Maya model of one is fairly significant too - if you're programming a real robot to move its manipulator around a robot cell and achieve a particular group of tasks, you can swap back and forward between FK and the two IK modes to get the head where you want, save the location in your program and move on to the next point, with the robot figuring out the best way between those points. the equivalent in Maya would be to set keyframes for the set points and let Maya interpolate between them. Relatively simple, except that to swap back and forward between control modes you'll need multiple joint systems that follow each other around, which is not easy to do without creating cyclic dependencies.
Not that I've tried it, but it shouldn't be too hard to set up a Mel script to make a user interface that works similarly to a real robot control pendant, once you've got the rest set up.
If you're after some good robot models, you can download them from the ABB website (they need to be converted to Maya format) - I'm pretty sure you can get the same sorts of things from Motoman, Fanuc and Kuka.
And as for your arm flipping out by +/-180 or +/-360 degrees, I've seen real robots try to do this while I've been perfecting some robot programs in factories I've set up! (A real robot locks up at this point, where Maya will actually flip out. Mainly on joint 5 & 6 in the real robots) At least in maya with a no flip knee set up you should be able to control this better.
Good luck with your robot, and if I can be of any assistance let me know!