Question:Which properties of the three radiations decides what use they can be put to?
It is mainly their differing penetrating powers.
The three types of radiation all have similar amount of energy. But they travel different distance through different materials.
If the radiation needs to penetrate some distance through a material only gamma is very useful.
On the other hand if we want to measure small changes in thickness of a thin piece of metal sheet, then beta radiation is more useful because its intensity is reduced more strongly by changes in thickness of the sheet.