Ideal opamp voltage?

it depends on the opamp your using.. you should check the datasheets and decide yourself..

18v should be fine.  Many of the op-amps that people roll can run from up to 36V rails, but there are some that have a lower maximum voltage.

Keep in mind that when you change the headphones, you are completely changing the load. 32 ohm Denon's and Grados obviously pull more current at the same output level than 600 ohm Beyers. I would check out the datasheets for the opamps you want to try and see what their recommended bias voltages are, then adjust the resistors to set the gain for a certain headphone.

Nah, changing the headphones doesn't directly affect the source, but if you are driving a 32 ohm load with a 5V peak-to-peak signal it will be most likely be much louder than driving a 600 ohm load with the same signal. High impedance headphones usually need higher gain.

Volume control typically works like a variable voltage divider scaling a "weak" input (like something coming from a DAC) to an opamp. I've never seen a volume control which scales the output. You would need a very beefy, very expensive, logarithmic potentiometer which can handle the full power of the amplifier. Anyways, the opamp doesn't care what the input signal is, it will simply apply a fixed gain determined by the ratio of various resistors. Usually the bias voltage is chosen so it's slightly above what the maximum output signal level can be, since the output voltage level cannot ever exceed the bias voltage. Outputs of "rail-to-rail" opamps can get very close to the bias voltage, but cannot actually ever reach it exactly.

Say you have a signal (sine wave, or whatever, doesn't matter) which is currently at exactly 1V coming from a DAC. You cut it in "half" (reduce by 3dB) by a volume knob and the gain of the opamp is set to -3. The output of the opamp will be at -1.5 volts. Gain is negative because inverting amplifiers tend to have slightly less distortion than non-inverting amplifiers due to common-mode rejection issues. With inverting amplifiers the non-inverting terminal is usually connected directly to signal ground, unless you are doing DC offset compensation with a resistor between the non-inverting terminal and ground, but that's another lesson for another day.

You now take that -1.5 volt output, and lets say you have a 32 ohm speaker, the current into 32 ohms from -1.5 volts is -47mA, or 70mW.

Now you plug in a 600 ohm speaker to the exact same system set to the exact same levels. The current into 600 ohms from -1.5 volts is -2.5mA or 3.75mW, which is obviously way different than 70mW. To find the output from the speaker you will need to know the sensitivity of your speaker, which is usually measured in dB per watt.

Bottom line, you will have to set the gain of the system so that at maximum volume (zero attenuation between your source and the amplifier) will be at your maximum listening level for a given speaker. 100dB is really loud, and could potentially damage hearing so I would be careful. Most headphone amplifiers I've seen have a gain in the -3 to -10 range, but it will strongly depend on the impedance of the load, the level of the source, etc...