How to precisely measure small charges?
If you use a transimpedance charge amplifier, the input capacitance of the amplifier is to a virtual ground so it only has an effect (to first order) on noise. 







simulate this circuit &ndash; Schematic created using CircuitLab

R1 provides a DC path for the bias current and should be very high value

Ignoring R1, output voltage change for input charge q is -q/C1 

The op-amp could be an electrometer type, but if you have no idea of the charge magnitude you might want to start with a $2.50 (or 0.25) one before  you use a $25 one.

Maybe try 100pF or 1nF and 10M (time constant 1ms/10ms) assuming that fits with the timing of your charge impulse. 

A decent fA bias current op-amp can probably provide a useful output with signals of 100uV or less, which represents a charge of 0.01pC with 100pF. You can add an amplification stage afterward if you want a bit more voltage- wide-bandwidth scopes tend to be pretty noisy even at x1. 

I suspect you have quite a bit of charge based on your ballpark description and you may  have to have more capacitance and/or series resistance to avoid damaging voltages- anothe reason to start with a cheaper socketed op-amp.