A small bomb, consisting of one stick of dynamite and a very small amount of radioactive material.
A medium size bomb, such as a backpack or small car filled with explosives and a greater amount of radioactive material.
A large bomb, such as a truck filled with explosives and a large amount of radioactive material High explosives such as dynamite are widely available.
The main limitation on a dirty bomb's ability to inflict severe radiation sickness would be the amount and concentration of the radioactive material used in the device.