Which particle decays are quickest?

Have a look here, on the four fundamental forces and ther typical interaction times.

The couplings are directly responsible for how fast a decay happens, bar some conservation rules for special cases.

The classification happened because of observing decay time differences similar to the difference between rho and pi0, and modelling mathematically the decays.

Decays happen when there exist lower energy particles to which an unstable particle can decay. The decay time is hierarchical, if hadrons are available, it is the strong decay that dominates the probability of decay, if quantum numbers allow it, the electromagnetic comes next. The weak appears when conservation of charge or other quantum numbers inhibits the electromagnetic. The gravitational one is very weak and not involved in particle decays.

The rho because it decays to two other hadrons has the characteristic strong decay. The pion in general, has the muon to decay to, so the charged ones go to a muon and muon antineutrino. There is no neutral muon, so the pi0 goes electromagnetically to two gammas.