Method: link ionization to charge, mass and range.
A charged particle strips electrons from atoms as it passes. The heavier and more highly charged the particle, and the shorter its range, the more concentrated its ionization becomes.
Rank the candidates by charge and speed. The alpha particle is doubly charged, $+2e$, and roughly four times heavier than a proton, so it lumbers through matter and dumps all its energy in a very short path of a few centimetres in air. That short, dense track means the most ion pairs per millimetre. Beta particles are singly charged and very light, so they zip through and ionize far less densely. Gamma photons carry no charge and only ionize through secondary electrons they occasionally kick out, so their direct ionizing action is smallest among the charged-versus-photon comparison. Neutrons, being neutral, also cause little direct ionization.
The ordering of ionizing strength is therefore alpha first by a wide margin. The trade-off is that this same short range makes alpha the least penetrating, easily stopped by paper or skin.
\[\boxed{\text{Alpha}}\]