Don't forget electrocorticography (ECoG), but it does require a 10 cm craniotomy. Its like EEG, but the electrodes are put on surface of the brain.
More seriously, I'll echo the instrumentation op-amp suggestion for either EMG or EEG. I recommend using an integrated circuit with all 3 op-amps on one chip. You can get chips where a single external resistor sets the gain of the amp. However, if you want to reduce environmental noise, you'll want to put the voltage follower op-amps of the instrumentaiton amp within a cm of the electrodes, in which case an IC would not be the best.
on limb electrodes with EEG:
EEG is very sensitive to the slightest movement of the subject. Putting electrodes elsewhere on the body can help detect movements, so that the signal can be corrected with independent component analysis (ICA), or the data during movements can be simply tossed out. Alternatively, muscle tone can very with depth of sleep, so it would be useful to record EMG in addition to EEG when studying levels of sleep and hypnosis.
Can some one suggest an affordable analog to digital converter with multiple channels?