Is there a rule of thumb for what to look at in the datasheets if fast saturation recovery is needed?
I think the parameter you wanted to consider is the Over Drive Recovery Time.When the amplifier is pushed into saturation, it takes time to recover and return to normal linear behavior.This time is defined as Over Drive Recovery.You can usually check this this characteristics on the TPC section of device data sheet.
For an instance you have an inverting configuration with again of 10 and rails of +/-15V.You can provide a step input of 2.25V.
Below is an example of Positive Over Drive Recovery.
Thanks and regards.
Some opamps do have this information on their datasheets (tables or graph), other do not. I just wanted to know if there is an indicator (like input type, RR, impedances etc.) to look for when filtering products by their parameters.