Can anyone thoroughly can suggest which design method for a schmitt trigger I should go for if I want some fast switching operation. As in on the basis of set thresholds, I would like to make the trigger as fast as to measure events which are impulse signals with a gap of nanoseconds which I guess makes the frequency in the range of GHz.

 

I think you'll most likely succeed with a fast comparator IC rather than discrete transistors or op amps; even the fastest op amps will likely fall far short of your speed requirements.

Analog Devices has a selection of fast comparators you might be able to use, as listed in this chart.

 

Can you really explain in terms of speeds and propagation delays on what should I go for?
My objective is to count signals from say, a photodiode. I am confused what to use after a transimpedence amplifier to keep a track on the individual events of photons striking on.
Also, I would need an equally faster transimpedence amplifier circuit too if say my light source is fast pulses. I don't have much experience on device models and all except I know how they function.

 

I wish I could help you more, but what you're attempting to do involves speeds a lot higher than anything I've ever worked with. The fastest transimpedance amplifier I've done is the one shown in the attachment in this post. It seems to me you're looking for something between one and three orders of magnitude faster.

All I can do is wish you luck. Maybe someone else has some ideas...