For the most part, Japanese white rice tastes like ass. And because of trade restrictions they cannot import large amounts of tastier and more nutritious rice from Southeast Asia.
Anyway, brown rice is available in pretty much any store. But it's usually sold in smaller 1 or 2kg bags. It's called "genmai" 玄米, and it's a bit more expensive. But way more tasty.
You can order supplements from
iHerb.com - Vitamins, Supplements & Natural Health Products. The shipping is really cheap, I buy a 5lb tub of protein once every few months, along with fish oil and creatine.
Milk and eggs are cheap as well. And, the cheapest milk is the full fat milk, usually the store brand is cheapest. You can get a litre for 150-180yen. Eggs are usually 150-200yen for 10, sometimes though you can find them for 100yen.
If you go to the store after 7pm you'll find meat and sushi on sale, often you can get meat for 20-30% off at that time. But usually you can find a store that sells chicken breasts for 35-45yen per 100g, which is dirt cheap.
You can also order meat from
Shopping/Online Shopping from Costco -- Import Groceries & Goods From this website you can order stuff from Costco, but the markup is about 20% and you have to pay for shipping. But even then, sometimes it's cheaper, or at least you can get a good variety. The frozen chicken breasts and ground meat are a good deal. Most of the other meats are expensive compared to the regular store.
Actually, there is a Costco in Fukuoka, you can get tons of stuff from there.