As I understand it, the Higgs-Boson itself is unstable and has a transient existence. So, the particle detectors cannot detect it directly. Instead, the detectors register all the decay products and from the data, this decay process is reconstructed. If the observed decay products match a possible decay channel of the Higgs-Boson it indicates the existence of the Higgs-Boson.
From what I have read, the two important decay channels used to prove the existence of the Higgs-Boson are the 'two-photon event' and the 'four-lepton event'. My questions are the following:
What is the exact decay process of the above two events and what exactly do the particles detectors detect? (or references for the same)
Why did we look for these particular events as there apparently are other decay channels as well which we could look for? (I understand that these events have a higher probability of occurrence, I want to know why exactly.)