Hallo Mak,

how many samples you need per pulse? Ten? Then sample/hold, conversion and storing (by your microcontroller, if you want to use one) have to be done in only 1µsec! So, you need something like AD671 or AD871 from Analog Devices.
But there is an additional problem. How to catch the pulse? If you use a schmitt-trigger with certain threshold, pulse has already started. Perhaps you can sample input voltage for 5msec (1/200Hz) at constant sampling rate of 1MHz. This gives you 5000 samples. Afterwards you can search the pulse and store.

Bye,
Kai