When doing my wireless guiltar project in uni, I measured the output of my SG up to 2V RMS...but then again, it could go very low. That was with a simple impedence buffer after it straight into an oscilloscope.
For your app, I would experiment with opamps, and power amplifiers.
I would say an opamp with variable gain and high input imepedence, followed by an audio power amplifier, such as the 'ol LM386.
The order would be 'opamp buffer -> opamp preamp (inverting if you wish to boost, or attenuate the signal, non-inverting if you only wish to amplify it, positive gain) -> headphone amp.
There are many example circuits of all the above three, so it would just be a case of experimenting, and plugging them altogether. I wouldn't worry about any form of EQ, its gain you need to work out.
If you really want to get fancy then you could add a simple 'clipping detector' to see if your gain is too high.
Blueteeth.
Ps. Gotta love the fender rhodes...I could spend all day playing one of those..