Just a few of my observations along the years. I am pretty sure you will find other opinions around.
If cost is not a factor, in general you are looking at the highest working temperature versus number of rated hours. Also, polymer or tantalum capacitors usually have a longer lifetime. In some cases you may need to carefully look at the ESR so you don't blow any diodes at power up. Also, sometimes you need to fit a capacitor in its alotted space, so the dimensions are important - IME ultra small capacitors always compromise on one or more of the prior specs above.
In certain spacious places you can also reduce the stress on the capacitor by using a higher voltage part.
One additional detail is that, in certain places, it may be tempting to replace a lower value electrolytic with a MLCC (they can potentially last forever). However, the circuit may be designed to work with the inferior frequency response of the electrolytic and therefore nowadays I only replace them with the same approximate type (sometimes poly or tantalum).