BpB, okay that makes sense now with the magnets glued to the fan. You said the voltage requirement of the fan was 12 volts, what are it's current requirements? If you can answer that question a proper answer can be provided.
I'm still a little confused because you keep talking about this being AC even though you specifically stated that the fan is a re-purposed PC fan which means it would be DC...
If this is truly a basic PC power supply fan like the 3-4 inch case fans that are so common then it won't draw more than 200ma of current. Virtually any old wire you have laying around can handle that current even old phone wire. You can use any 12 volt wall wart that can supply at least that much current. I did a quick simulation with a 60ohm resistor as a load and you'd be fine with a 500ohm rheostat/pot that can handle 1watt (max power dissipation would be 600mw) the exact value/power rating you'd need will depend on the exact specs for your fan.
If you have trouble finding a rheostat/pot that will work you can always simply use a multi position switch to switch in strings of 20-100ohm resistors. The power drop with resistance is exponential so you'd switch in a 20ohm resistor first, then, 40, then 80, 160, 320, 640 to get a roughly linear power drop and stirrers really don't need to have infinitely variable speeds 5-6 speeds should be fine. An audio taper pot/rheostat would be required to get a linear feel to the knob as well but that's just what's ideal not what's required.
By the way Jagura thanks for the correction, I'll try to remember that =)