After reading about your Chernobyl experience and fears I have two tips. First first aid kit or drinking water tabs are not safe to take as a substitute for proper thyroid blocking Potassium Iodide or Iodate. If you are stuck without the proper Iodide or Iodate there is research indicating that 8 ml of 2% iodine (iodine tincture, Betadine, etc) solution painted onto the forearm or abdomen two hours before exposure will be absorbed and give a blocking initial dose. DO NOT SWALLOW IODINE SINCE IT IS POISONOUS IF INGESTED. IT MUST ONLY BE APPLIED TO SKIN!!!
You can buy crystalline KI powder if you feel that buying iodide tablets is too expensive, but the solution must then be diluted, masked, or encapsulated as it is horribly bitter when eaten/drunk straight.
A person must have a way of measuring radiation, a proper Geiger counter is best, preferably one designed to measure high level radiation as most non civil defenseor military will only measure very low dose. The CD  models are available cheap and often include a low dose counter, a high dose counter and 8 dosimeter pens with a dosimeter calibrator. I personally keep a Nukalert keychain scintillator counter (always on for 10 years) and a pocket dosimeter in my bag along with some KI. If you haven’t the funds for a Geiger counter a dosimeter can be made which will allow you to seek a lower radiation area. The page http://www.ki4u.com/free_book/s60p792.htm  gives instructions based on a design in the children’s science book “Build It Yourself Science Laboratory” from 1963 by Raymond Barrett. This device is a hack job to be used by the unprepared in emergencies only, it doesn’t easily give you a real read on the radiation just that it is present but is better than no detector.
Protecting food from radionuclides is best accomplished through green housing and filtering water. Water filters are cheaply available now in the micron level, a heavy metals filter would impart more protection. Ground water will be one of your lowest concern for radionuclides though.
Greenhousing is cheap and easy if you are already used to gardening. It can make your garden output explode! UV resistant plastic sheet, mounted on heavy PVC pipe frame with several poles sunk into the ground for support make an excellent greenhouse. Lay perforated hose under the rows for growing and connect to a water source. Cover the ground with plastic to minimize weeds and water loss leaving small holes for the baby plants to grow through. As your vine type plants grow, hang rope for them to climb and help them twist around these ropes. You will massively increase your season, save water the Israeli way (we feed all of Europe from desert greenhouses) and protect your food from all kinds of contamination that drops from the air. Compost all your organic waste and save it for next year before you lay your new plastic sheet onto the ground.
JWR’s Comment: The Kearney Fallout Meter (see: Nuclear War Survival Skills –available for free download) is another “quick and dirty” design. However, keep in mind that any improvised fallout meter is a poor substitute for a proper dosimeter, rate meter, and Geiger counter commercially built to NRC specifications. Buy a set! Someday you’ll be glad that you did. Guru says: “Poor Prior Planning Produces Pitifully Poor Performance” (P7) OBTW, Nukalerts are available from ReadyMadeResources.com  and several other Internet vendors.