The antioxidant combination most commonly used in radiation research in recent years has been a mixture of:
Selenomethionine. (A source of selenium, a component of the important natural antioxidant glutathione peroxidase. The standard dose is 200 micrograms of selenium per day. A dose of much more than 400 micrograms of selenium per day causes a risk of serious selenium toxicity.)
N-Acetyl Cysteine. (Safe, and often very beneficial, for most people in ongoing daily doses of 800 milligrams or more, especially when used in conjuction with vitamin C. The only concern for the ongoing use of this nutrient would be for those rare individuals who tend to form cystine kidney stones. If you are one of those individuals, you probably already know it.  Most kidney stones are not made up of cystine. Those who tend to form cystine kidney stones usually have a specific genetic disorder.)
Ascorbic acid (vitamin C). The quantity of vitamin C, in milligrams, should be at least 4 times the number of IU (International Units) of vitamin E. Vitamin C is quite safe, even in large doses for short periods of time. Studies have shown that some people seem to develop problems from ongoing doses in excess of 2000 milligram per day over long periods. Extremely large doses have been used intravenously for short periods of time. Some doctors and dentists have given 20 to 40 gram doses intravenously during surgical and dental procedures to promote wound healing.  In general, it is best to limit oral dosages to 2000 milligrams per day except during unusual circumstances (such as a radiation emergency, where you may want to use more).
Alpha tocopherol succinate. (Vitamin E.) (In general tests of vitamin E as a nutritional supplement, gamma tocopherol succinate has been shown to be safer and much more effective than the alpha form. The alpha form of the vitamin, however, is the one that has been most commonly used in the past; and it is the one that has been commonly used in radiation testing.)
Co-enzyme Q-10. (If you are buying this for any kind of long-term storage, be sure to get it in powdered form. Co-enzyme Q-10 is more readily absorbed from the oil-filled capsules, but these are unlikely to be suitable for any kind of long-term storage.)
Alpha Lipoic Acid. (R-lipoic acid should work just as well, and is at least twice as effective as alpha lipoic acid in most antioxidant tests; but R-lipoic acid costs a lot more.)
Melatonin. Melatonin is a very powerful and safe antioxidant that is necessary to maintain a normal sleep cycle (which also happens to be something that is likely to be disrupted during a disaster). A reasonable dosage during a radiation disaster is 10 mg. or more before bedtime. Although much larger doses are safe, larger doses may cause drowsiness the next day in many people. If you don't already know how you will respond to melatonin, it is a good idea to try various doses to determine how you will react to it before taking large nightly doses in a disaster situation. Many people (myself included) use melatonin on a nightly basis even in normal situations.
A very important nutritional supplement with powerful protection against radiation is DIM (diindolylmethane). DIM is a natural metabolite of certain compounds found in certain vegetables, such as broccoli and cabbage, that has been available as a nutritional supplement for many years. The powerful radiological protection provided by DIM has only been discovered in very recent years. It appears that most of the radiation protection provided by DIM is not due to the antioxidant mechanism. The optimal dosage of DIM for radiation protection is unknown. It is commonly available in capsules of about 100 milligrams. During times of a significant radiation disaster, it appears to be quite safe to take dosages of one or two of these capsules every one to two waking hours. One capsule 3 times a day may be all that is needed during lesser radiation emergencies. DIM is best absorbed if taken with foods containing fats or oils.
I wish that I could find all of the above supplement in a single capsule. So far, however, nothing like this has appeared on the market that would be suitable for a radiation emergency, although there are several good antioxidant supplements on the market for normal situations. In general medical studies, the best results from alpha lipoic acid have come from using the time-released formulations (also called sustained-release). The one that I have routinely been using is Jarrow brand Alpha Lipoic Sustain in 300 milligram tablets. These should be taken at level of at least 3 tablets a day in a radiation emergency. (This 900 milligram per day of sustained-release alpha lipoic acid has also been shown in medical studies to stabilize blood sugar levels, which may be very useful since blood sugar fluctuations can often be a problem for many people in disaster situations.)
The brand of DIM that I personally use is Source Naturals 100 mg. tablets. I have no justification for using this brand other than relatively low cost for such a powerful radiation protectant and easy availability of the brand.
I always take a higher dose of these nutrients, especially DIM, before I have a CT scan. CT scans are very useful medically, but they also expose the individual to much higher doses of ionizing radiation than common x-rays.
Brown, Stephen L., et al. (April 2010), "Antioxidant Diet Supplementation Starting 24 Hours after Exposure Reduces Radiation Lethality" Radiation Research. Vol. 173, Issue 4, pages 462-468.
Kennedy, A.R., et al. (July 2011), "Suppression of the later stages of radiation-induced carcinogenesis by antioxidant dietary formulations." Radiation Research. Vol. 176, Issue 1, pages 62-70.
SHIRAZI., A., et al. (July, 2007), "A Radiobiological Review on Melatonin: A Novel Radioprotector" Journal of Radiation Research. Vol. 48, Issue 4, pages 263-272.
Connell, P.P. and Weichselbaum R.R. (November 12, 2013) "Small molecule derived from a natural product that mitigates radiation injury" Proceedings of the National Academies of Science, U.S.A. Vol. 110, Issue 46, pages 18355-18356.
Fan, S. et al. (November 12, 2013) "DIM (3,3'-diindolylmethane) confers protection against ionizing radiation by a unique mechanism" Proceedings of the National Academies of Science, U.S.A. Vol. 110, Issue 46, pages 18650-18655.