Since you may want to detect the edge of your pulse with sufficient resolution, you may want something even faster than a few hundred MHz. See the attached link for a few tips on how to choose an oscilloscope; I think pages 6 and 7 are particularly illuminating, showing how the detected signal changes depending on the sampling rate of the oscilloscope.
If you want to measure also the pulse duration with a certain accuracy you need a high bandwith scope with at least a factor 10 higher sampling rate than the pulse width.
To measure our 2ns Nd-YAG laser pulses we use a 8 Gs/s scope (1GHz input bandwidth) and a ultrafast photodiode (Alphalas, risetime 250ps). Input impedance of the scope (50 Ohms) and the photodiode hace to be matched.
Take care not to artificially increase pulse width by allowing reflections of the beam (on other lab equipment) to reach the photodiode as this can seemingly increase pulsewidth (light pulse runtime is also in the range of nanoseconds).
The response time is very important. The response time of your photodetector should be faster than 2 ns, and the bandwith of the oscilloscope of 500 MHz.
The most important thing is that the oscilloscope bandwidth must be greater than 1/T where T is the pulsewidth. So you need a scope with about one GHz bandwidth. You need also that photo detector capacitance Cd to be very small to make with the transimpedance amplifier resistance Rf a time consatnt Cd Rf that must be smaller than the pulse width of the optical narrow pulse. So, Also about i ns time constant may be suitable to great extent. The more safe condition not to shape the pulse is a rise time about T/10.
To see the effect of the Cd and Rf on the optical pulses please see the paper in the link: Conference Paper A comprehensive study of an optical transceiver