This circuit doesn't need to maximize capacitance, rather it needs to make sure that the impedance is lowest when it matters the most.
If you choose electrolytic, its Equivalent Series Resistance at high audio frequencies is the most relevant spec.
Tantalums are usually good at higher frequencies, it seems.
But I would use film capacitors, the largest reasonable value. Or ceramic caps. You might do the math on lower values; those in the circuit may have been chosen for convenience and not performance. Certainly since this is a headphone amp, you need quiet. If I used electrolytics I would have a 1uF ceramic in parallel with them.
[edit] Oh, and the feedback network is arbitrary. If the op amp has a high input impedance you can change it to 220K/10K and decrease C2 by a factor of ten.[\edit]