Order of emission of radioactive particles

Is there any sort of sequence in the emission of radioactive particles? ie. alpha, beta, gamma or any other type of decay I don't know about.

Specifically, I wanted to know is there any evidence to support the fact that there is a gamma decay immediately after a beta-particle decay? And if so, is there any reason for this? And also, is the energy of every gamma decay the same?

First, while $\beta$ particles were identified early in the study of radioactive decay, the classic $\beta$ particle is a high-energy electron, part of $\beta$ - decay. Such an electron does not usually produce $\gamma$ radiation.
On the other hand, $\beta$ + decay produces a positron, and this will quickly encounter an electron, the two will annihilate, and a pair of 511 keV photons will be produced. And yes, 511 keV is $\gamma$ radiation.
As to your larger question, the answer is, "sort of, but not really". Generally speaking, $\gamma$ radiation is at the end of many decay chains, so you can sort of consider it the last in the sequence, except that electron/positron pair production occurs when a 1.022 MeV + photon hits an atom, so there's no absolute rule.
$\alpha$ (helium nuclei) and $\beta$ (electrons or positrons) processes are not ordinarily sequential, so it's not appropriate to talk about one occurring before the other.