How to select the best opamp for a constant current MOSFET driver
I would pick something like the LT1056 with specified low output impedance since you're only isolating the output with 10\$\Omega\$. It's not particularly cheap. If you want to reduce cost, you can put the work in to search for your important parameters (30V operating voltage, relatively high slew rate and GBW etc.) 



Depending on the polarity of the offset voltage of the op-amp you happen to get, the output could rail at the negative supply and then take a long time to slew back to 0V, so you can put a 1N4148 across the feedback capacitor. Speaking of which, you probably want to reduce that to maybe 1nF to speed up the response.