I believe that the content of radioactive substances in food depends mainly on where we get the food from. Radioactive materials enter food from its surroundings. Plants and mushrooms get radioactivity from the soil they grow in and animals have radioactive particles in them either from food (plants) or air/water.

Some plants accumulate more particles (including radioactive ones) than others — typical examples are mushrooms, which we discussed in an earlier answer (link), or bananas (link).

Fish absorb a lot of radioactive elements from animals. The principle of preserving radioactivity can be clearly seen in fish — fish usually contain a lot of iodine (and therefore it is healthy to eat them), but in the case that  a radioactive isotope of iodine (e.g. I 131) is dispersed in the water rather than the usual isotope of iodine (I 127), this radioactive iodine settles in the body of the fish as easily as regular iodine. The fish’s body will function normally (containing the necessary iodine), but due to the decay of the radioactive isotope of iodine, the cells in the fish’s body will be irradiated. As it is dangerous for us to eat radioactive foods, e.g. radioactive fish, after consuming it, the content of radioactive iodine in the thyroid gland will increase at the expense of the usual iodine.

But there is nothing to worry about — the limits of the content of radioactive substances are set very strictly and food is also checked for the content of radionuclides. Therefore, we do not face any major danger when consuming freely available food.