If I could get a ceramic capacitor at the capacitance of 10uF and within my voltage requirements, which from my initial searches I can, what problems would I experience if I were to change, if any?
Some circuits (like some linear regulators, for example), require a certain minimum ESR from the output capacitor, which could cause the circuit to oscillate when using a ceramic but not with an electrolytic.
In a precision circuit, a ceramic might not be preferred due to microphonics, but in those cases you probably wouldn't want an electrolytic either.
Otherwise, ceramics are generally preferred. They'll have lower ESR, they're not polarized, they need less voltage de-rating, and so on.
Finally, when searching SMD footprint standards, the common packages seem to be 0402, 0603, and 0805, where they increase in physical size respectively, but also power rating, which suggests to me I should use as large of a package as possible
Usually you choose the smallest package you can get away with because you want to fit as much circuit as you can in the smallest footprint.
Also, for ceramics, the larger sizes (1210 and higher) can have reliability issues because they can be cracked if the board flexes.
Though it depends on your specific caps, all the very low leakage caps I have bought for precision low drift integrators (time constants of 1 second or more) were metal polyester film. They were also very stable over temperature compared to ceramic disk, which often stated +80 -20% over the commercial temperature range.
They are good for high frequency as well and the ones you show are quite high manufacturing quality. Just don't use the physically big ones to bypass. The leads will be too long or the distance from the part will defeat the purpose.
Best Answer
For audio applications (as opposed to decoupling) there really aren't any high frequency transients to deal with, so a capacitor with a self-resonant frequency well above the audio range should be sufficient.
An electrolytic capacitor is of course polarized, and only useful if the DC+signal is always unipolar. Also, an electrolytic capacitor has a shorter lifetime than many other types.
A ceramic capacitor in the high capacitance dielectric types will have significant change in capacitance with applied voltage. This can add distortion in audio applications.
A film capacitor isn't very space efficient, but it is reliable, non-polarized and has very good performance in audio applications.