If temperature is not an issue, what can be said about the different ceramic dielectrics
Even if ambient temperature is well controlled, air currents can cause noise if there is significant voltage across the capacitor. 

Capacitance degradation with time is different for different dielectrics. And the big one, voltage coefficient of capacitance. 

If you can use them, NP0 caps suffer from such effects much less than X5R X7R etc. parts, but they are simply not available or are very large and expensive in higher values. There are plenty of cases where an X7R cap in the signal path works just fine. On the other hand, I've used NP0 parts as bypass caps in special applications. 

Another characteristic is that smaller parts, especially when you approach the limits of what is possible within a given footprint, tend to have a high voltage coefficient, so most of the capacitance (as much as 80%) can simply disappear when biased at a normal operating voltage. So it may be better to use an 0805 or 0603 rather than a 0402 or 0201 even if they are bigger and possibly more expensive. 



The data sheets are  usually incomplete, but some manufacturers offer much more complete data in the form of online or locally generated data individual to each part. For example, this Murata site (requires Flash) allows you to extract CSV data for various characteristics.