The hifi guys are more nuts on this subject, but I'll give you in a capsule the more-or-less accepted rules of thumb. I do hate to see the hifi tweako mystique infiltrating the musical and effects arena... sigh...
For tonal qualities, caps are largely chosen by their dielectric absorption.
The semi-accepted order is:
teflon - thought to sound ultimately clear, use for circuit boards too
polystyrene - ditto
polycarbonate - ditto minus a hair
polypropylene - ditto, plus available in uF sizes
polyester (mylar) - Ok if you can't get something better, not a lot worse than the
other plastic films, and much better than those lower in the list
NPO ceramic - only available in tiny sizes
aluminum electrolytic - the accepted standard for uF and
up sizes simply on $ and size
paper - obsolete, can't get them anymore
thought to be "tweedy" or some such
other ceramic types - thought to sound "grainy"
tantalum - unreliable and thought to sound
Above teflon is vacuum then air, which are impractical for all normal circuits. There exist other exotica, like glass dielectric capacitors for special purposes.
There are capacitance size and voltage limits, obviously. 100uF polystyrene caps don't exist, while aluminum is barely working up a sweat at 100uF. Likewise, there are no 1000V aluminums, but 1Kv ceramics are easy and cheap. Also the construction of the capacitor, whether stacked, rolled, folded, extended tab, etc., etc., can have real effects (as distinguished from silliness like cryogenic stress relief or water jacketing).
I personally have staged a couple of capacitor shootouts, and haven't yet found someone who could tell simply by listening whether they were hearing music through a polypropylene versus ceramic, although I don't doubt that someone might be able to.
"Best sounding in FX" is not something you can nail down, as you will find that each person may perceive "better" and "best" as meaning something different. I'd be willing to make a significant bet with you that I could set up a test where I changed only the capacitor and you would not be able to do more than 50% +/- 2% correct telling the caps apart by sound alone.
IMHO you would be wasting your money chasing down and buying super premium caps for effects. Use mylar and aluminum, get it working, and when it's going good, substitute out for some super-premium stuff until you satisfy your curiosity. On the other hand, don't just use the high-value ceramic caps for audio coupling (even though many highly sought after vintage effects did exactly this).

There are people who disagree with me strenuously, even violently.